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Dutta R, Cabral DGA, Lyu N, Vu NP, Wang Y, Allen B, Dan X, Cortiñas RG, Khazaei P, Schäfer M, Albornoz ACCD, Smart SE, Nie S, Devoret MH, Mazziotti DA, Narang P, Wang C, Whitfield JD, Wilson AK, Hendrickson HP, Lidar DA, Pérez-Bernal F, Santos LF, Kais S, Geva E, Batista VS. Simulating Chemistry on Bosonic Quantum Devices. J Chem Theory Comput 2024. [PMID: 39068594 DOI: 10.1021/acs.jctc.4c00544] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this Perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Delmar G A Cabral
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Nam P Vu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
- Department of Chemistry, Lafayette College, Easton, Pennsylvania 18042, United States
| | - Yuchen Wang
- Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Brandon Allen
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Xiaohan Dan
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Rodrigo G Cortiñas
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Pouya Khazaei
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Max Schäfer
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Alejandro C C D Albornoz
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Scott E Smart
- Division of Physical Sciences, College of Letters and Science and Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Scott Nie
- Division of Physical Sciences, College of Letters and Science and Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Michel H Devoret
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
| | - Prineha Narang
- Division of Physical Sciences, College of Letters and Science and Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Chen Wang
- Department of Physics, University of Massachusetts - Amherst, Amherst, Massachusetts 01003, United States
| | - James D Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 01003, United States
| | - Angela K Wilson
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48864, United States
| | - Heidi P Hendrickson
- Department of Chemistry, Lafayette College, Easton, Pennsylvania 18042, United States
| | - Daniel A Lidar
- Department of Electrical & Computer Engineering, Department of Chemistry, Department of Physics & Astronomy, and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, United States
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
| | - Lea F Santos
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, United States
| | - Sabre Kais
- Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
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Luo YX, Cong LJ, Zheng ZG, Liu HY, Ming Y, Yang RC. Entanglement enhancement and EPR steering based on a PT-symmetric-like cavity-opto-magnomechanical hybrid system. OPTICS EXPRESS 2023; 31:34764-34778. [PMID: 37859225 DOI: 10.1364/oe.500854] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/19/2023] [Indexed: 10/21/2023]
Abstract
We investigate the enhancement of entanglement and EPR steering in a parity-time(PT-) symmetric-like cavity-opto-magnomechanical system. The system consists of an optical cavity, a magnon mode in a ferromagnetic crystal, a phonon mode, and a microwave cavity. Our findings demonstrate that microwave-cavity gain significantly boosts distant quantum entanglement and greatly improves the robustness of bipartite entanglement against environment temperature. Additionally, we observe an enhancement of tripartite entanglement within the system and uncover the phenomenon of entanglement transfer. Notably, we also achieve one-way steering and two-way asymmetric steering in the system. This study offers insights into the integration of traditional optomechanics and cavity magnomechanics, presenting a novel approach to manipulate asymmetric quantum steering between two distant macroscopic objects. The implications of our research extend to the fields of quantum state preparation and quantum information.
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Satoori S, Mahdavifar S, Vahedi J. Entanglement and quantum correlations in the XX spin-1/2 honeycomb lattice. Sci Rep 2022; 12:17991. [PMID: 36289302 PMCID: PMC9606302 DOI: 10.1038/s41598-022-19945-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 09/06/2022] [Indexed: 11/16/2022] Open
Abstract
The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two powerful numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the quantum discord (QD) among nearest-neighbor spins. We show that the quantum correlations can capture the position of the quantum critical points in the whole range of the ground state phase diagram consistent with previous results. Although the concurrence and the QD are short-range, informative about long-ranged critical correlations. In addition, we address a ”magnetic-entanglement” behavior that starts from an entangled field around the saturation field.
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Affiliation(s)
- Sahar Satoori
- grid.411872.90000 0001 2087 2250Department of Physics, University of Guilan, 41335-1914 Rasht, Iran
| | - Saeed Mahdavifar
- grid.411872.90000 0001 2087 2250Department of Physics, University of Guilan, 41335-1914 Rasht, Iran
| | - Javad Vahedi
- grid.15078.3b0000 0000 9397 8745Department of Physics and Earth Sciences, Jacobs University Bremen, Bremen, 28759 Germany
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Dong L, Bao J, Guo B, Sun Z. Quantum nonlocality and topological quantum phase transitions in the extended Ising chain. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:425405. [PMID: 35952634 DOI: 10.1088/1361-648x/ac8905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Accepted: 08/11/2022] [Indexed: 06/15/2023]
Abstract
We use two-site quantum nonlocality to identify the topological quantum phase transitions (TQPTs) of the extended Ising model driven by varying system parameters. We investigate how the system parameters, including the anisotropies of the nearest-neighbor and the next-nearest-neighbor spin pairs, the transverse magnetic field, and the three-spin interaction, affect the quantum nonlocality. We show that the nonlocality cannot mark any TQPTs while its first derivative can perfectly characterize the TQPTs. By making the influences of the thermal fluctuations and the site distance of spin pairs on the critical behavior of the TQPTs analysis, we show that the sufficiently low temperature has a slight impact on the features of nonlocality and its first derivative while the site distance of spin pairs can significantly alter the properties of nonlocality and its first derivative. We further present the energy spectra and the trajectories of the winding vectors of the model to demonstrate that the quantum nonlocality can be employed to successfully signalize the TQPTs.
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Affiliation(s)
- Luzhao Dong
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Jia Bao
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Bin Guo
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Zhaoyu Sun
- School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430023, People's Republic of China
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De Vriendt X, Van Hende D, De Baerdemacker S, Bultinck P, Acke G. Uncovering phase transitions that underpin the flat-planes in the tilted Hubbard model using subsystems and entanglement measures. J Chem Phys 2022; 156:244115. [DOI: 10.1063/5.0092153] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The failure of many approximate electronic structure methods can be traced to their erroneous description of fractional charge and spin redistributions in the asymptotic limit toward infinity, where violations of the flat-plane conditions lead to delocalization and static correlation errors. Although the energetic consequences of the flat-planes are known, the underlying quantum phase transitions that occur when (spin)charge is redistributed have not been characterized. In this study, we use open subsystems to redistribute (spin)charges in the tilted Hubbard model by imposing suitable Lagrange constraints on the Hamiltonian. We computationally recover the flat-plane conditions and quantify the underlying quantum phase transitions using quantum entanglement measures. The resulting entanglement patterns quantify the phase transition that gives rise to the flat-plane conditions and quantify the complexity required to accurately describe charge redistributions in strongly correlated systems. Our study indicates that entanglement patterns can uncover those phase transitions that have to be modeled accurately if the delocalization and static correlation errors of approximate methods are to be reduced.
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Affiliation(s)
- Xeno De Vriendt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Daria Van Hende
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Stijn De Baerdemacker
- Department of Chemistry, University of New Brunswick, 30 Dineen Drive, Fredericton, New Brunswick E3B 5A3, Canada
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Guillaume Acke
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
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6
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Phases of the Bose–Einstein Condensate Dark Matter Model with Both Two- and Three-Particle Interactions. UNIVERSE 2021. [DOI: 10.3390/universe7100359] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper, we further elaborate on the Bose–Einstein condensate (BEC) dark matter model extended in our previous work [Phys. Rev. D 2020, 102, 083510] by the inclusion of sixth-order (or three-particle) repulsive self-interaction term. Herein, our goal is to complete the picture through adding to the model the fourth-order repulsive self-interaction. The results of our analysis confirm the following: while in the previous work the two-phase structure and the possibility of first-order phase transition was established, here we demonstrate that with the two self-interactions involved, the nontrivial phase structure of the enriched model remains intact. For this to hold, we study the conditions which the parameters of the model, including the interaction parameters, should satisfy. As a by-product and in order to provide some illustration, we obtain the rotation curves and the (bipartite) entanglement entropy for the case of a particular dwarf galaxy.
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Bao J, Liu YH, Guo B. Global quantum discord in the Lipkin-Meshkov-Glick model at zero and finite temperatures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:495401. [PMID: 34517354 DOI: 10.1088/1361-648x/ac2647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 09/13/2021] [Indexed: 06/13/2023]
Abstract
We study the global quantum discord (GQD) in the Lipkin-Meshkov-Glick (LMG) model at zero and finite temperatures, in which all spins are mutually interacted and introduced in an external magnetic field (denoted byh). We confirm that the high coordinate number is one of the most distinguishing features of the LMG model, which directly results in the nontrivial behaviors of quantum correlations. We compare the GQD with other quantum correlations measures (such as concurrence, quantum discord, and global entanglement) and find the remarkable difference between them. For instance, we find that GQD spreads in the entire system and captures more information on quantum correlations when comparing with concurrence and quantum (pairwise) discord. We discover that GQD can characterize multipartite correlations in the both broken phase (h< 1) and the symmetric phase (h⩾ 1), while global entanglement and its generalized fail. Moreover, we show that the ground-state GQD can identify second-order quantum phase transitions of the LMG model in the thermodynamic limit. By making the scaling behavior of the GQD in the LMG model analysis, we show that GQD (denoted byG) scales asG∼k⋅N+cwithk> 0 in the anisotropic cases for any fixed magnetic field. We further show that GQD behaves asG|sn∼k⋅1N+cwithk< 0 in the isotropic cases for any Dicke state |sn⟩. Hereinkandcare the fitting parameters. We also find that the thermal stability of the GQD at low temperatures depends on the energy gap. We further reveal that the extraordinary behaviors of the thermal-state GQD in the isotropic LMG model are explained by the contribution theory of the energy levels.
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Affiliation(s)
- Jia Bao
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Yan-Hong Liu
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Bin Guo
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
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Jing J, Guidry M, Wu LA. An anomaly in quantum phases induced by borders. Sci Rep 2020; 10:6934. [PMID: 32332877 PMCID: PMC7181724 DOI: 10.1038/s41598-020-63555-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2019] [Accepted: 03/17/2020] [Indexed: 11/09/2022] Open
Abstract
AbstractThe stationary behavior of a quantum system is determined by its Hamiltonian and its boundary conditions. All quantum phase transitions (QPT) reported previously were induced by changing the Hamiltonian. In a circular spin model with Heisenberg XY interactions and no magnetic field, we observe an anomaly in quantum phases caused by a qualitative change of the boundary condition. The unexpected anomaly features an infinite number of single-particle levels, in the same pattern as the single-photon-triggered quantum phase transition in the Rabi model.
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Bahovadinov MS, Gülseren O, Schnack J. Local entanglement and string order parameter in dimerized models. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:505602. [PMID: 31487699 DOI: 10.1088/1361-648x/ab41b5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this letter, we propose an application of string order parameter (SOP), commonly used in quantum spin systems, to identify symmetry-protected topological phase (SPT) in fermionic systems in the example of the dimerized fermionic chain. As a generalized form of dimerized model, we consider a one-dimensional spin-1/2 XX model with alternating spin couplings. We employ Jordan-Wigner fermionization to map this model to the spinless Su-Schrieffer-Heeger fermionic model (SSH) with generalized hopping signs. We demonstrate a phase transition between a trivial insulating phase and the Haldane phase by the exact analytical evaluation of reconstructed SOPs which are represented as determinants of Toeplitz matrices with the given generating functions. To get more insight into the topological quantum phase transition (tQPT) and microscopic correlations, we study the pairwise concurrence as a local entanglement measure of the model. We show that the first derivative of the concurrence has a non-analytic behaviour in the vicinity of the tQPT, like in the second order trivial QPTs.
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Affiliation(s)
- Murod S Bahovadinov
- Department of Physics, Bilkent University, 06800, Bilkent, Ankara, Turkey. Fakultät für Physik, Universität Bielefeld, D-33501 Bielefeld, Germany
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Hagymási I, Hubig C, Legeza Ö, Schollwöck U. Dynamical Topological Quantum Phase Transitions in Nonintegrable Models. PHYSICAL REVIEW LETTERS 2019; 122:250601. [PMID: 31347875 DOI: 10.1103/physrevlett.122.250601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Revised: 05/14/2019] [Indexed: 06/10/2023]
Abstract
We consider sudden quenches across quantum phase transitions in the S=1 XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.
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Affiliation(s)
- I Hagymási
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Budapest H-1525, P.O. Box 49, Hungary
| | - C Hubig
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
| | - Ö Legeza
- Strongly Correlated Systems "Lendület" Research Group, Institute for Solid State Physics and Optics, MTA Wigner Research Centre for Physics, Budapest H-1525, P.O. Box 49, Hungary
| | - U Schollwöck
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics (ASC), Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
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Abstract
By employing quantum renormalization group (QRG) method, we investigate quantum phase transitions (QPT) in the Ising transverse field (ITF) model and in the XXZ Heisenberg model, with and without Dzyaloshinskii Moriya (DM) interaction, on a periodic chain of N lattice sites. We adopt a new approach called spin squeezing as an indicator of QPT. Spin squeezing, through analytical expression of a spin squeezing parameter, is calculated after each step of QRG. As the scale of the system becomes larger, (after many QRG steps), the ground state (GS) spin squeezing parameters show an abrupt change at a quantum critical point (QCP). Moreover, in all of the studied models, the first derivative of the spin squeezing parameter with respect to the control parameter is discontinuous, which is a signature of QPT. The spin squeezing parameters develop their saturated values after enough QRG iterations. The divergence exponent of the first derivative of the spin squeezing parameter in the near vicinity of the QCP is associated with the critical exponent of the correlation length.
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Gabbrielli M, Smerzi A, Pezzè L. Multipartite Entanglement at Finite Temperature. Sci Rep 2018; 8:15663. [PMID: 30353077 PMCID: PMC6199326 DOI: 10.1038/s41598-018-31761-3] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2018] [Accepted: 08/17/2018] [Indexed: 11/10/2022] Open
Abstract
The interplay of quantum and thermal fluctuations in the vicinity of a quantum critical point characterizes the physics of strongly correlated systems. Here we investigate this interplay from a quantum information perspective presenting the universal phase diagram of the quantum Fisher information at a quantum phase transition. Different regions in the diagram are identified by characteristic scaling laws of the quantum Fisher information with respect to temperature. This feature has immediate consequences on the thermal robustness of quantum coherence and multipartite entanglement. We support the theoretical predictions with the analysis of paradigmatic spin systems showing symmetry-breaking quantum phase transitions and free-fermion models characterized by topological phases. In particular we show that topological systems are characterized by the survival of large multipartite entanglement, reaching the Heisenberg limit at finite temperature.
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Affiliation(s)
- Marco Gabbrielli
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy
| | - Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125, Firenze, Italy.
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De Chiara G, Sanpera A. Genuine quantum correlations in quantum many-body systems: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:074002. [PMID: 29671752 DOI: 10.1088/1361-6633/aabf61] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.
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Affiliation(s)
- Gabriele De Chiara
- Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
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Cheng JQ, Xu JB. Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpiński fractal lattices. Phys Rev E 2018; 97:062134. [PMID: 30011478 DOI: 10.1103/physreve.97.062134] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Indexed: 11/07/2022]
Abstract
We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpiński fractal lattices by employing the multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of the multipartite entanglement and quantum coherence exhibit singular behaviors, and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpiński fractal lattices. Furthermore, the dimensions determine the relations between the critical exponents and the correlation length exponents for these lattices.
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Affiliation(s)
- Jun-Qing Cheng
- Zhejiang Institute of Modern Physics and Physics Department, Zhejiang University, Hangzhou 310027, China
| | - Jing-Bo Xu
- Zhejiang Institute of Modern Physics and Physics Department, Zhejiang University, Hangzhou 310027, China
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15
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Pezzè L, Gabbrielli M, Lepori L, Smerzi A. Multipartite Entanglement in Topological Quantum Phases. PHYSICAL REVIEW LETTERS 2017; 119:250401. [PMID: 29303346 DOI: 10.1103/physrevlett.119.250401] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2017] [Indexed: 06/07/2023]
Abstract
We witness multipartite entanglement in the ground state of the Kitaev chain-a benchmark model of a one dimensional topological superconductor-also with variable-range pairing, using the quantum Fisher information. Phases having a finite winding number, for both short- and long-range pairing, are characterized by a power-law diverging finite-size scaling of multipartite entanglement. Moreover, the occurring quantum phase transitions are sharply marked by the divergence of the derivative of the quantum Fisher information, even in the absence of a closing energy gap.
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Affiliation(s)
- Luca Pezzè
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Marco Gabbrielli
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - Luca Lepori
- Dipartimento di Scienze Fisiche e Chimiche, Università dell'Aquila, via Vetoio 42, I-67010 Coppito-L'Aquila, Italy
- INFN, Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, I-67100 Assergi (AQ), Italy
| | - Augusto Smerzi
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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16
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Frazão HM, de Faria JGP, Pellegrino GQ, Nemes MC. Quantum phase transition in an effective three-mode model of interacting bosons. Phys Rev E 2017; 96:062146. [PMID: 29347450 DOI: 10.1103/physreve.96.062146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2017] [Indexed: 06/07/2023]
Abstract
In this work we study an effective three-mode model describing interacting bosons. These bosons can be considered as exciton-polaritons in a semiconductor microcavity at the magic angle. This model exhibits quantum phase transition (QPT) when the parameters of the corresponding Hamiltonian are continuously varied. The properties of the Hamiltonian spectrum (e.g., the distance between two adjacent energy levels) and the phase space structure of the thermodynamic limit of the model are used to indicate QPT. The relation between spectral properties of the Hamiltonian and the corresponding classical frame of the thermodynamic limit of the model is established as indicative of QPT. The average number of bosons in a specific mode and the entanglement properties of the ground state as functions of the parameters are used to characterize the order of the transition and also to construct a phase diagram. Finally, we verify our results for experimental data obtained for a setting of exciton-polaritons in a semiconductor microcavity.
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Affiliation(s)
- H M Frazão
- Universidade Federal do Piauí, Campus Profa. Cinobelina Elvas, Bom Jesus, PI, Brazil
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
| | - J G Peixoto de Faria
- Departamento de Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil
| | - G Q Pellegrino
- Departamento de Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil
| | - M C Nemes
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
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17
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Radhakrishnan C, Parthasarathy M, Jambulingam S, Byrnes T. Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions. Sci Rep 2017; 7:13865. [PMID: 29066775 PMCID: PMC5655009 DOI: 10.1038/s41598-017-13871-6] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Accepted: 09/06/2017] [Indexed: 11/23/2022] Open
Abstract
We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The σzσz interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and find similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.
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Affiliation(s)
- Chandrashekar Radhakrishnan
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai, 200122, China. .,NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China.
| | - Manikandan Parthasarathy
- Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai, 600004, India
| | - Segar Jambulingam
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai, 200122, China.,Department of Physics, Ramakrishna Mission Vivekananda College, Mylapore, Chennai, 600004, India
| | - Tim Byrnes
- New York University Shanghai, 1555 Century Ave, Pudong, Shanghai, 200122, China. .,NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China. .,State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai, 200062, China. .,National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan. .,Department of Physics, New York University, New York, NY, 10003, USA.
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18
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Cheng WW, Wang XY, Sheng YB, Gong LY, Zhao SM, Liu JM. Finite-temperature scaling of trace distance discord near criticality in spin diamond structure. Sci Rep 2017; 7:42360. [PMID: 28198404 PMCID: PMC5309762 DOI: 10.1038/srep42360] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2016] [Accepted: 01/08/2017] [Indexed: 11/09/2022] Open
Abstract
In this work we explore the quantum correlation quantified by trace distance discord as a measure to analyze the quantum critical behaviors in the Ising-XXZ diamond structure at finite temperatures. It is found that the first-order derivative of the trace distance discord exhibits a maximum around the critical point at finite temperatures. By analyzing the finite-temperature scaling behavior, we show that such a quantum correlation can detect exactly the quantum phase transitions from the entan-gled state in ferrimagnetic phase to an unentangled state in ferrimagnetic phase or to an unentangled state in ferromagnetic phase. The results also indicate that the above two kinds of transitions can be distinguished by the different finite-temperature scaling behaviors. Moreover, we find that the trace distance discord, in contrast to other typical quantum correlations (e.g., concurrence, quantum discord and Hellinger distance), may be more reliable to exactly spotlight the critical points of this model at finite temperatures under certain situations.
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Affiliation(s)
- W W Cheng
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - X Y Wang
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - Y B Sheng
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - L Y Gong
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China.,National Laboratory of Solid State Microstructures &Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - S M Zhao
- Institute of Signal Processing &Transmission, Nanjing University of Posts and Telecommunication, Nanjing, 210003, China
| | - J M Liu
- National Laboratory of Solid State Microstructures &Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
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19
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Lin YC, Yang PY, Zhang WM. Non-equilibrium quantum phase transition via entanglement decoherence dynamics. Sci Rep 2016; 6:34804. [PMID: 27713556 PMCID: PMC5054423 DOI: 10.1038/srep34804] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Accepted: 09/20/2016] [Indexed: 01/05/2023] Open
Abstract
We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained.
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Affiliation(s)
- Yu-Chen Lin
- Department of Physics and Centre for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
| | - Pei-Yun Yang
- Department of Physics and Centre for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
| | - Wei-Min Zhang
- Department of Physics and Centre for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
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20
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21
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Phase diagram of quantum critical system via local convertibility of ground state. Sci Rep 2016; 6:29175. [PMID: 27381284 PMCID: PMC4933908 DOI: 10.1038/srep29175] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Accepted: 06/15/2016] [Indexed: 11/08/2022] Open
Abstract
We investigate the relationship between two kinds of ground-state local convertibility and quantum phase transitions in XY model. The local operations and classical communications (LOCC) convertibility is examined by the majorization relations and the entanglement-assisted local operations and classical communications (ELOCC) via Rényi entropy interception. In the phase diagram of XY model, LOCC convertibility and ELOCC convertibility of ground-states are presented and compared. It is shown that different phases in the phase diagram of XY model can have different LOCC or ELOCC convertibility, which can be used to detect the quantum phase transition. This study will enlighten extensive studies of quantum phase transitions from the perspective of local convertibility, e.g., finite-temperature phase transitions and other quantum many-body models.
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22
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Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction. Sci Rep 2016; 6:19359. [PMID: 26780973 PMCID: PMC4726107 DOI: 10.1038/srep19359] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Accepted: 12/11/2015] [Indexed: 11/08/2022] Open
Abstract
We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions.
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23
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Misra A, Biswas A, Pati AK, Sen De A, Sen U. Quantum correlation with sandwiched relative entropies: Advantageous as order parameter in quantum phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052125. [PMID: 26066137 DOI: 10.1103/physreve.91.052125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2014] [Indexed: 06/04/2023]
Abstract
Quantum discord is a measure of quantum correlations beyond the entanglement-separability paradigm. It is conceptualized by using the von Neumann entropy as a measure of disorder. We introduce a class of quantum correlation measures as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative Rényi and Tsallis entropies. We compare our results with those obtained by using the traditional relative entropies. We find that the measures satisfy all the plausible axioms for quantum correlations. We evaluate the measures for shared pure as well as paradigmatic classes of mixed states. We show that the measures can faithfully detect the quantum critical point in the transverse quantum Ising model and find that they can be used to remove an unquieting feature of nearest-neighbor quantum discord in this respect. Furthermore, the measures provide better finite-size scaling exponents of the quantum critical point than the ones for other known order parameters, including entanglement and information-theoretic measures of quantum correlations.
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Affiliation(s)
- Avijit Misra
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Anindya Biswas
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Arun K Pati
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Aditi Sen De
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Ujjwal Sen
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
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24
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Hemmatiyan S, Rahimi Movassagh M, Ghassemi N, Kargarian M, Rezakhani AT, Langari A. Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:155601. [PMID: 25812634 DOI: 10.1088/0953-8984/27/15/155601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the 'perturbative continuous unitary transformations' approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.
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Affiliation(s)
- S Hemmatiyan
- Department of Physics, Texas A&M University, College Station, TX 77843-4242, USA. Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
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25
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Factorization and Criticality in the Anisotropic XY Chain via Correlations. ENTROPY 2015. [DOI: 10.3390/e17020790] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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26
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Scaling of geometric quantum discord close to a topological phase transition. Sci Rep 2014; 4:4473. [PMID: 24667280 PMCID: PMC3966051 DOI: 10.1038/srep04473] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2013] [Accepted: 03/10/2014] [Indexed: 11/08/2022] Open
Abstract
Quantum phase transition is one of the most interesting aspects in quantum many-body systems. Recently, geometric quantum discord has been introduced to signature the critical behavior of various quantum systems. However, it is well-known that topological quantum phase transition can not be described by the conventional Landau's symmetry breaking theory, and thus it is unknown that whether previous study can be applicable in this case. Here, we study the topological quantum phase transition in Kitaev's 1D p-wave spinless quantum wire model in terms of its ground state geometric quantum discord. The derivative of geometric quantum discord is nonanalytic at the critical point, in both zero temperature and finite temperature cases. The scaling behavior and the universality are verified numerically. Therefore, our results clearly show that all the key ingredients of the topological phase transition can be captured by the nearest neighbor and long-range geometric quantum discord.
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27
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McDonald CR, Orlando G, Abraham JW, Hochstuhl D, Bonitz M, Brabec T. Theory of the quantum breathing mode in harmonic traps and its use as a diagnostic tool. PHYSICAL REVIEW LETTERS 2013; 111:256801. [PMID: 24483751 DOI: 10.1103/physrevlett.111.256801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2012] [Indexed: 06/03/2023]
Abstract
An analytical expression for the quantum breathing frequency ωb of harmonically trapped quantum particles with inverse power-law repulsion is derived. It is verified by ab initio numerical calculations for electrons confined in a lateral (2D) quantum dot. We show how this relation can be used to express the ground state properties of harmonically trapped quantum particles as functions of the breathing frequency by presenting analytical results for the kinetic, trap, and repulsive energy and for the linear entropy. Measurement of ωb together with these analytical relations represents a tool to characterize the state of harmonically trapped interacting particles--from the Fermi gas to the Wigner crystal regime.
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Affiliation(s)
- C R McDonald
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada
| | - G Orlando
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada
| | - J W Abraham
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - D Hochstuhl
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - T Brabec
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N6N5, Canada
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28
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Zhu Z, Huse DA, White SR. Weak plaquette valence bond order in the S = 1/2 honeycomb J1 - J2 Heisenberg model. PHYSICAL REVIEW LETTERS 2013; 110:127205. [PMID: 25166840 DOI: 10.1103/physrevlett.110.127205] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2013] [Indexed: 06/03/2023]
Abstract
Using the density matrix renormalization group, we investigate the S = 1/2 Heisenberg model on the honeycomb lattice with first (J(1)) and second (J(2)) neighbor interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For J(2)/J(1) near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for J(2) ≲ 0.26 and by a valence bond crystal for J(2) ≳ 0.36. The longest correlation length that we find in this intermediate phase is for plaquette valence bond order. This correlation length grows strongly with cylinder circumference, indicating either quantum criticality or weak plaquette valence bond order.
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Affiliation(s)
- Zhenyue Zhu
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
| | - David A Huse
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Steven R White
- Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
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29
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Zhang J, Wei TC, Laflamme R. Experimental quantum simulation of entanglement in many-body systems. PHYSICAL REVIEW LETTERS 2011; 107:010501. [PMID: 21797528 DOI: 10.1103/physrevlett.107.010501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2011] [Revised: 05/08/2011] [Indexed: 05/31/2023]
Abstract
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudoentanglement. The observed pseudoentanglement for a small-size system already displays a singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.
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Affiliation(s)
- Jingfu Zhang
- Institute for Quantum Computing, Department of Physics, University of Waterloo, Ontario, Canada
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30
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Werlang T, Trippe C, Ribeiro GAP, Rigolin G. Quantum correlations in spin chains at finite temperatures and quantum phase transitions. PHYSICAL REVIEW LETTERS 2010; 105:095702. [PMID: 20868176 DOI: 10.1103/physrevlett.105.095702] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2010] [Revised: 07/15/2010] [Indexed: 05/29/2023]
Abstract
We compute the quantum correlation [quantum discord (QD)] and the entanglement (EOF) between nearest-neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EOF and other thermodynamic quantities, spotlight the critical points associated with quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.
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Affiliation(s)
- T Werlang
- Departamento de Física, Universidade Federal de São Carlos, São Carlos, SP 13565-905, Brazil
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31
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Costa Farias RJ, de Oliveira MC. Entanglement and the Mott insulator--superfluid phase transition in bosonic atom chains. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:245603. [PMID: 21393788 DOI: 10.1088/0953-8984/22/24/245603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We analyze the developing of bipartite and multipartite entanglement through the Mott insulator-superfluid quantum phase transition. Starting from a Mott insulator state, where a filling factor ν = N/M = 1 per lattice site is considered, we derive an expression for a completely connected graph configuration of bosons and show how bipartite and multipartite entanglement evolve through the phase transition predicted in previous works. We show how, in the transition, bipartite entanglement is distributed through the system respecting monogamous relations.
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Affiliation(s)
- R J Costa Farias
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, 13083-970, Campinas--SP, Brazil.
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32
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Pal AK, Bose I. Entanglement in a molecular three-qubit system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:016004. [PMID: 21386239 DOI: 10.1088/0953-8984/22/1/016004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study the entanglement properties of a molecular three-qubit system described by the Heisenberg spin Hamiltonian with anisotropic exchange interactions and including an external magnetic field. The system exhibits first-order quantum phase transitions by tuning two parameters, x and y, of the Hamiltonian to specific values. The three-qubit chain is open-ended so that there are two types of pairwise entanglement: nearest-neighbour (nn) and next-nearest-neighbour (nnn). We calculate the ground and thermal state concurrences, quantifying pairwise entanglement, as a function of the parameters x, y and the temperature T. The entanglement threshold and gap temperatures are also determined as a function of the anisotropy parameter x. The results obtained are of relevance in understanding the entanglement features of the recently engineered molecular Cr(7)Ni-Cu(2+)-Cr(7)Ni complex which serves as a three-qubit system at sufficiently low temperatures.
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33
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Facchi P, Marzolino U, Parisi G, Pascazio S, Scardicchio A. Phase transitions of bipartite entanglement. PHYSICAL REVIEW LETTERS 2008; 101:050502. [PMID: 18764381 DOI: 10.1103/physrevlett.101.050502] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2007] [Indexed: 05/26/2023]
Abstract
We analyze the statistical properties of the entanglement of a large bipartite quantum system. By framing the problem in terms of random matrices and a fictitious temperature, we unveil the existence of two phase transitions, characterized by different spectra of the reduced density matrices.
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Affiliation(s)
- P Facchi
- Dipartimento di Matematica, Università di Bari, Bari, Italy
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34
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França VV, Capelle K. Entanglement in spatially inhomogeneous many-fermion systems. PHYSICAL REVIEW LETTERS 2008; 100:070403. [PMID: 18352528 DOI: 10.1103/physrevlett.100.070403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2007] [Indexed: 05/26/2023]
Abstract
We investigate entanglement of strongly interacting fermions in spatially inhomogeneous environments. To quantify entanglement in the presence of spatial inhomogeneity, we propose a local-density approximation (LDA) to the entanglement entropy, and a nested LDA scheme to evaluate the entanglement entropy on inhomogeneous density profiles. These ideas are applied to models of electrons in superlattice structures with different modulation patterns, electrons in a metallic wire in the presence of impurities, and phase-separated states in harmonically confined many-fermion systems, such as electrons in quantum dots and atoms in optical traps. We find that the entanglement entropy of inhomogeneous systems is strikingly different from that of homogeneous systems.
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Affiliation(s)
- V V França
- Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
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35
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Zanardi P, Giorda P, Cozzini M. Information-theoretic differential geometry of quantum phase transitions. PHYSICAL REVIEW LETTERS 2007; 99:100603. [PMID: 17930382 DOI: 10.1103/physrevlett.99.100603] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2007] [Indexed: 05/25/2023]
Abstract
The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum phase transitions featured by the corresponding system. This approach provides a universal conceptual framework to study quantum critical phenomena which is differential geometric and information theoretic at the same time.
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Affiliation(s)
- Paolo Zanardi
- Department of Physics and Astronomy, University of Southern California Los Angeles, California 90089-0484, USA
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36
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Campos Venuti L, Zanardi P. Quantum critical scaling of the geometric tensors. PHYSICAL REVIEW LETTERS 2007; 99:095701. [PMID: 17931018 DOI: 10.1103/physrevlett.99.095701] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2007] [Indexed: 05/25/2023]
Abstract
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.
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Affiliation(s)
- Lorenzo Campos Venuti
- Institute for Scientific Interchange, Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy
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37
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Legeza O, Sólyom J, Tincani L, Noack RM. Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases. PHYSICAL REVIEW LETTERS 2007; 99:087203. [PMID: 17930977 DOI: 10.1103/physrevlett.99.087203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2006] [Revised: 05/10/2007] [Indexed: 05/25/2023]
Abstract
We propose a new approach to study quantum phase transitions in low-dimensional fermionic or spin models that go from uniform to spatially inhomogeneous phases such as dimerized, trimerized, or incommensurate phases. It is based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.
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Affiliation(s)
- O Legeza
- Research Institute for Solid State Physics and Optics, H-1525, Budapest, Hungary
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de Oliveira TR, Rigolin G, de Oliveira MC, Miranda E. Multipartite entanglement signature of quantum phase transitions. PHYSICAL REVIEW LETTERS 2006; 97:170401. [PMID: 17155445 DOI: 10.1103/physrevlett.97.170401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2006] [Indexed: 05/12/2023]
Abstract
We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.
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Affiliation(s)
- Thiago R de Oliveira
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, CEP 13083-970, Campinas, São Paulo, Brazil.
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Zanardi P, Paunković N. Ground state overlap and quantum phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031123. [PMID: 17025610 DOI: 10.1103/physreve.74.031123] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2006] [Revised: 05/31/2006] [Indexed: 05/12/2023]
Abstract
We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and XY models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as with the dynamical study of the Loschmidt echo for critical systems.
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Affiliation(s)
- Paolo Zanardi
- Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy
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Quan HT, Song Z, Liu XF, Zanardi P, Sun CP. Decay of Loschmidt echo enhanced by quantum criticality. PHYSICAL REVIEW LETTERS 2006; 96:140604. [PMID: 16712060 DOI: 10.1103/physrevlett.96.140604] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2005] [Indexed: 05/09/2023]
Abstract
We study the transition of a quantum system from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system E coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of E modeled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of E strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing S vanish sharply.
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Affiliation(s)
- H T Quan
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China
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Legeza O, Sólyom J. Two-site entropy and quantum phase transitions in low-dimensional models. PHYSICAL REVIEW LETTERS 2006; 96:116401. [PMID: 16605844 DOI: 10.1103/physrevlett.96.116401] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2005] [Revised: 01/04/2006] [Indexed: 05/08/2023]
Abstract
We propose a new approach to study quantum phase transitions in low-dimensional lattice models. It is based on studying the von Neumann entropy of two neighboring central sites in a long chain. It is demonstrated that the procedure works equally well for fermionic and spin models, and the two-site entropy is a better indicator of quantum phase transition than calculating gaps, order parameters, or the single-site entropy. The method is especially convenient when the density-matrix renormalization-group algorithm is used.
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Affiliation(s)
- O Legeza
- Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary
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Chen K, Albeverio S, Fei SM. Entanglement of formation of bipartite quantum states. PHYSICAL REVIEW LETTERS 2005; 95:210501. [PMID: 16384121 DOI: 10.1103/physrevlett.95.210501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2005] [Indexed: 05/05/2023]
Abstract
We give an explicit tight lower bound for the entanglement of formation for arbitrary bipartite mixed states by using the convex hull construction of a certain function. This is achieved by revealing a novel connection among the entanglement of formation, the well-known Peres-Horodecki, and realignment criteria. The bound gives a quite simple and efficiently computable way to evaluate quantitatively the degree of entanglement for any bipartite quantum state.
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Affiliation(s)
- Kai Chen
- Institut für Angewandte Mathematik, Universität Bonn, D-53115, Germany
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Larsson D, Johannesson H. Entanglement scaling in the one-dimensional Hubbard model at criticality. PHYSICAL REVIEW LETTERS 2005; 95:196406. [PMID: 16384005 DOI: 10.1103/physrevlett.95.196406] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Indexed: 05/05/2023]
Abstract
We derive exact expressions for the local entanglement entropy epsilon in the ground state of the one-dimensional Hubbard model at a quantum phase transition driven by a change in magnetic field h or chemical potential mu. The leading divergences of delta epsilon/delta h and delta epsilon/delta mu are shown to be directly related to those of the zero-temperature spin and charge susceptibilities. Logarithmic corrections to scaling signal a change in the number of local states accessible to the system as it undergoes the transition.
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Affiliation(s)
- Daniel Larsson
- Department of Physics, Göteborg University, SE 412 96 Göteborg, Sweden
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Chen K, Albeverio S, Fei SM. Concurrence of arbitrary dimensional bipartite quantum states. PHYSICAL REVIEW LETTERS 2005; 95:040504. [PMID: 16090790 DOI: 10.1103/physrevlett.95.040504] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2005] [Indexed: 05/03/2023]
Abstract
We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.
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Affiliation(s)
- Kai Chen
- Institut für Angewandte Mathematik, Universität Bonn, Germany
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Roscilde T, Verrucchi P, Fubini A, Haas S, Tognetti V. Entanglement and factorized ground states in two-dimensional quantum antiferromagnets. PHYSICAL REVIEW LETTERS 2005; 94:147208. [PMID: 15904106 DOI: 10.1103/physrevlett.94.147208] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2004] [Indexed: 05/02/2023]
Abstract
Making use of exact results and quantum Monte Carlo data for the entanglement of formation, we show that the ground state of anisotropic two-dimensional S=1/2 antiferromagnets in a uniform field takes the classical-like form of a product state for a particular value and orientation of the field, at which the purely quantum correlations due to entanglement disappear. Analytical expressions for the energy and the form of such states are given, and a novel type of exactly solvable two-dimensional quantum models is therefore singled out. Moreover, we show that the field-induced quantum phase transition present in the models is unambiguously characterized by a cusp minimum in the pairwise-to-global entanglement ratio R, marking the quantum-critical enhancement of multipartite entanglement.
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Affiliation(s)
- Tommaso Roscilde
- Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA
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