1
|
Hales J, Bajpai U, Liu T, Baykusheva DR, Li M, Mitrano M, Wang Y. Witnessing light-driven entanglement using time-resolved resonant inelastic X-ray scattering. Nat Commun 2023; 14:3512. [PMID: 37316515 DOI: 10.1038/s41467-023-38540-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2022] [Accepted: 05/03/2023] [Indexed: 06/16/2023] Open
Abstract
Characterizing and controlling entanglement in quantum materials is crucial for the development of next-generation quantum technologies. However, defining a quantifiable figure of merit for entanglement in macroscopic solids is theoretically and experimentally challenging. At equilibrium the presence of entanglement can be diagnosed by extracting entanglement witnesses from spectroscopic observables and a nonequilibrium extension of this method could lead to the discovery of novel dynamical phenomena. Here, we propose a systematic approach to quantify the time-dependent quantum Fisher information and entanglement depth of transient states of quantum materials with time-resolved resonant inelastic x-ray scattering. Using a quarter-filled extended Hubbard model as an example, we benchmark the efficiency of this approach and predict a light-enhanced many-body entanglement due to the proximity to a phase boundary. Our work sets the stage for experimentally witnessing and controlling entanglement in light-driven quantum materials via ultrafast spectroscopic measurements.
Collapse
Affiliation(s)
- Jordyn Hales
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
| | - Utkarsh Bajpai
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA
| | - Tongtong Liu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | | | - Mingda Li
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Matteo Mitrano
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA.
| | - Yao Wang
- Department of Physics and Astronomy, Clemson University, Clemson, SC, 29634, USA.
| |
Collapse
|
2
|
Baykusheva DR, Kalthoff MH, Hofmann D, Claassen M, Kennes DM, Sentef MA, Mitrano M. Witnessing Nonequilibrium Entanglement Dynamics in a Strongly Correlated Fermionic Chain. PHYSICAL REVIEW LETTERS 2023; 130:106902. [PMID: 36962013 DOI: 10.1103/physrevlett.130.106902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2022] [Revised: 01/13/2023] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
Many-body entanglement in condensed matter systems can be diagnosed from equilibrium response functions through the use of entanglement witnesses and operator-specific quantum bounds. Here, we investigate the applicability of this approach for detecting entangled states in quantum systems driven out of equilibrium. We use a multipartite entanglement witness, the quantum Fisher information, to study the dynamics of a paradigmatic fermion chain undergoing a time-dependent change of the Coulomb interaction. Our results show that the quantum Fisher information is able to witness distinct signatures of multipartite entanglement both near and far from equilibrium that are robust against decoherence. We discuss implications of these findings for probing entanglement in light-driven quantum materials with time-resolved optical and x-ray scattering methods.
Collapse
Affiliation(s)
| | - Mona H Kalthoff
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Damian Hofmann
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Martin Claassen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Dante M Kennes
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
- Institut für Theorie der Statistischen Physik, RWTH Aachen University, 52056 Aachen, Germany and JARA-Fundamentals of Future Information Technology, 52056 Aachen, Germany
| | - Michael A Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science (CFEL), Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Matteo Mitrano
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| |
Collapse
|
3
|
Zhou HQ, Shi QQ, Dai YW. Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer's Principle. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1306. [PMID: 36141191 PMCID: PMC9498036 DOI: 10.3390/e24091306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Revised: 08/04/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer's principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models-the quantum spin-1/2 XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-1/2 XYZ model, the quantum spin-1/2 XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-1/2 Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.
Collapse
Affiliation(s)
- Huan-Qiang Zhou
- Centre for Modern Physics, Chongqing University, Chongqing 400044, China
| | | | | |
Collapse
|
4
|
Gálisová L, Kaczor M. Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising-Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids. ENTROPY 2021; 23:e23121671. [PMID: 34945977 PMCID: PMC8700496 DOI: 10.3390/e23121671] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Revised: 12/03/2021] [Accepted: 12/08/2021] [Indexed: 11/25/2022]
Abstract
The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin-1/2 Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.
Collapse
Affiliation(s)
- Lucia Gálisová
- Institute of Manufacturing Management, Faculty of Manufacturing Technologies with the Seat in Prešov, Technical University of Košice, Bayerova 1, 080 01 Prešov, Slovakia
- Correspondence:
| | - Michał Kaczor
- The Doctoral School of University of Rzeszów, University of Rzeszów, Rejtana 16C, 35-935 Rzeszów, Poland;
- Insitute of Physics, College of Natural Sciences, University of Rzeszów, Rejtana 16A, 35-935 Rzeszów, Poland
| |
Collapse
|
5
|
Laurell P, Scheie A, Mukherjee CJ, Koza MM, Enderle M, Tylczynski Z, Okamoto S, Coldea R, Tennant DA, Alvarez G. Quantifying and Controlling Entanglement in the Quantum Magnet Cs_{2}CoCl_{4}. PHYSICAL REVIEW LETTERS 2021; 127:037201. [PMID: 34328778 DOI: 10.1103/physrevlett.127.037201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Revised: 05/18/2021] [Accepted: 05/25/2021] [Indexed: 06/13/2023]
Abstract
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
Collapse
Affiliation(s)
- Pontus Laurell
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Science and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Allen Scheie
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Chiron J Mukherjee
- Science Department, Drew School, San Francisco, California 94115, USA
- Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | | | | | | | - Satoshi Okamoto
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Radu Coldea
- Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D Alan Tennant
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Shull-Wollan Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Gonzalo Alvarez
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Science and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| |
Collapse
|
6
|
Probing resonating valence bond states in artificial quantum magnets. Nat Commun 2021; 12:993. [PMID: 33579921 PMCID: PMC7881118 DOI: 10.1038/s41467-021-21274-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Accepted: 01/15/2021] [Indexed: 11/08/2022] Open
Abstract
Designing and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations. The resonating valence bond state is a spin-liquid state where spins continuously alter their singlet partners. Here Yang et al. use spin-1/2 atoms precision-placed by a scanning tunnelling microscope to create artificial quantum magnets exhibiting the resonating valence bond state.
Collapse
|
7
|
Gray J, Banchi L, Bayat A, Bose S. Machine-Learning-Assisted Many-Body Entanglement Measurement. PHYSICAL REVIEW LETTERS 2018; 121:150503. [PMID: 30362777 DOI: 10.1103/physrevlett.121.150503] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Indexed: 06/08/2023]
Abstract
Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose a machine-learning-assisted scheme to measure the entanglement between arbitrary subsystems of size N_{A} and N_{B}, with O(N_{A}+N_{B}) measurements, and without any prior knowledge of the state. The method exploits a neural network to learn the unknown, nonlinear function relating certain measurable moments and the logarithmic negativity. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many-body systems in both equilibrium and nonequilibrium regimes.
Collapse
Affiliation(s)
- Johnnie Gray
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Leonardo Banchi
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Abolfazl Bayat
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
| | - Sougato Bose
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| |
Collapse
|
8
|
Vanherck J, Sorée B, Magnus W. Anisotropic bulk and planar Heisenberg ferromagnets in uniform, arbitrarily oriented magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:275801. [PMID: 29781444 DOI: 10.1088/1361-648x/aac65f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-2D magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane and easy-axis anisotropic ferromagnet-both in two and three dimensions-subjected to a uniform magnetic field, applied along an arbitrary direction. In this paper, a spin-[Formula: see text] Heisenberg Hamiltonian with anisotropic exchange interactions is solved using double-time temperature-dependent Green's functions and the Tyablikov decoupling approximation. We determine various magnetic properties such as the Curie temperature and the magnetization as a function of temperature and the applied magnetic field, discussing the impact of the system's dimensionality and the type of anisotropy. The magnetic reorientation transition taking place in anisotropic Heisenberg ferromagnets is studied in detail. Importantly, spontaneous magnetization is found to be absent for easy-plane 2D spin systems with short range interactions.
Collapse
Affiliation(s)
- Joren Vanherck
- Physics Department, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium. Imec, Kapeldreef 75, B-3001 Leuven, Belgium
| | | | | |
Collapse
|
9
|
Bera A, Das T, Sadhukhan D, Singha Roy S, Sen De A, Sen U. Quantum discord and its allies: a review of recent progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:024001. [PMID: 28824014 DOI: 10.1088/1361-6633/aa872f] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.
Collapse
Affiliation(s)
- Anindita Bera
- Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India. Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211019, India
| | | | | | | | | | | |
Collapse
|
10
|
Cerezo M, Rossignoli R, Canosa N, Ríos E. Factorization and Criticality in Finite XXZ Systems of Arbitrary Spin. PHYSICAL REVIEW LETTERS 2017; 119:220605. [PMID: 29286784 DOI: 10.1103/physrevlett.119.220605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2017] [Indexed: 06/07/2023]
Abstract
We analyze ground state (GS) factorization in general arrays of spins s_{i} with XXZ couplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GSs can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero-bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid for d-dimensional arrays. The definite magnetization-projected GSs at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization-compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.
Collapse
Affiliation(s)
- M Cerezo
- Instituto de Física de La Plata, CONICET, and Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata 1900, Argentina
| | - R Rossignoli
- Instituto de Física de La Plata, CONICET, and Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata 1900, Argentina
- Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CIC), La Plata 1900, Argentina
| | - N Canosa
- Instituto de Física de La Plata, CONICET, and Departamento de Física, Universidad Nacional de La Plata, C.C. 67, La Plata 1900, Argentina
| | - E Ríos
- Departamento de Ingeniería Química, Universidad Tecnológica Nacional, Facultad Regional Avellaneda, C.C. 1874, Argentina
| |
Collapse
|
11
|
Sadhukhan D, Roy SS, Rakshit D, Prabhu R, Sen De A, Sen U. Quantum discord length is enhanced while entanglement length is not by introducing disorder in a spin chain. Phys Rev E 2016; 93:012131. [PMID: 26871048 DOI: 10.1103/physreve.93.012131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2015] [Indexed: 06/05/2023]
Abstract
Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.
Collapse
Affiliation(s)
- Debasis Sadhukhan
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Sudipto Singha Roy
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - Debraj Rakshit
- Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
| | - R Prabhu
- 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
| |
Collapse
|
12
|
Liu JH, Shi QQ, Wang HL, Links J, Zhou HQ. Universal construction of order parameters for translation-invariant quantum lattice systems with symmetry-breaking order. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:020102. [PMID: 23005705 DOI: 10.1103/physreve.86.020102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2012] [Indexed: 06/01/2023]
Abstract
For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in terms of the fidelity between a ground state and its symmetry-transformed counterpart, and are computed through tensor network representations of the ground-state wave function. To illustrate our scheme, we consider three quantum systems on an infinite lattice in one spatial dimension, namely, the quantum Ising model in a transverse magnetic field, the quantum spin-1/2XYX model in an external magnetic field, and the quantum spin-1 XXZ model with single-ion anisotropy. All these models have symmetry group Z(2) and exhibit broken-symmetry phases. We also discuss the role of the order parameters in identifying factorized states.
Collapse
Affiliation(s)
- Jin-Hua Liu
- Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, People's Republic of China
| | | | | | | | | |
Collapse
|
13
|
Gualdi G, Giampaolo SM, Illuminati F. Modular entanglement. PHYSICAL REVIEW LETTERS 2011; 106:050501. [PMID: 21405382 DOI: 10.1103/physrevlett.106.050501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2010] [Revised: 11/07/2010] [Indexed: 05/30/2023]
Abstract
We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and noninteracting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.
Collapse
Affiliation(s)
- Giulia Gualdi
- Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy
| | | | | |
Collapse
|
14
|
Zhao JH, Wang HL, Li B, Zhou HQ. Spontaneous symmetry breaking and bifurcations in ground-state fidelity for quantum lattice systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:061127. [PMID: 21230664 DOI: 10.1103/physreve.82.061127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2010] [Indexed: 05/30/2023]
Abstract
Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground-state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry, occurs when some control parameter crosses its critical value. It is unveiled that the ground-state fidelity per lattice site exhibits such a bifurcation for quantum lattice systems undergoing quantum phase transitions. The significance of this result lies in the fact that the ground-state fidelity per lattice site is universal, in the sense that it is model independent, in contrast to (model-dependent) order parameters. This fundamental quantity may be computed by exploiting the developed tensor network algorithms on infinite-size lattices. We illustrate the scheme in terms of the quantum Ising model in a transverse magnetic field and the spin-1/2 XYX model in an external magnetic field on an infinite-size lattice in one spatial dimension.
Collapse
Affiliation(s)
- Jian-Hui Zhao
- Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, People's Republic of China
| | | | | | | |
Collapse
|
15
|
Luzanov AV, Prezhdo O. High-order entropy measures and spin-free quantum entanglement for molecular problems. Mol Phys 2010. [DOI: 10.1080/00268970701725039] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
16
|
Abouie J, Langari A, Siahatgar M. Thermodynamic behavior of the XXZ Heisenberg s = 1/2 chain around the factorizing magnetic field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:216008. [PMID: 21393734 DOI: 10.1088/0953-8984/22/21/216008] [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 have investigated the zero-and finite-temperature behaviors of the anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of a transverse magnetic field (h). The attention is concentrated on an interval of magnetic field between the factorizing field (h(f)) and the critical one (h(c)). The model presents a spin-flop phase for 0 < h < h(f) with an energy scale which is defined by the long range antiferromagnetic order while it undergoes an entanglement phase transition at h = h(f). The entanglement estimators clearly show that the entanglement is lost exactly at h = h(f), which justifies different quantum correlations on both sides of the factorizing field. As a consequence of zero entanglement (at h = h(f)) the ground state is known exactly as a product of single-particle states which is the starting point for initiating a spin wave theory. The linear spin wave theory is implemented to obtain the specific heat and thermal entanglement of the model in the interested region. A double-peak structure is found in the specific heat around h = h(f), which manifests the existence of two energy scales in the system as a result of two competing orders before the critical point. These results are confirmed by the low temperature Lanczos data which we have computed.
Collapse
Affiliation(s)
- J Abouie
- Department of Physics, Shahrood University of Technology, Shahrood 36199-95161, Iran.
| | | | | |
Collapse
|
17
|
Giampaolo SM, Adesso G, Illuminati F. Probing quantum frustrated systems via factorization of the ground state. PHYSICAL REVIEW LETTERS 2010; 104:207202. [PMID: 20867055 DOI: 10.1103/physrevlett.104.207202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2009] [Revised: 04/20/2010] [Indexed: 05/29/2023]
Abstract
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.
Collapse
Affiliation(s)
- Salvatore M Giampaolo
- Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, CNR-SPIN, CNISM, Unità di Salerno, and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy
| | | | | |
Collapse
|
18
|
Giampaolo SM, Adesso G, Illuminati F. Theory of ground state factorization in quantum cooperative systems. PHYSICAL REVIEW LETTERS 2008; 100:197201. [PMID: 18518481 DOI: 10.1103/physrevlett.100.197201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2008] [Indexed: 05/26/2023]
Abstract
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows us to determine rigorously the existence, location, and exact form of separable ground states in a large variety of, generally nonexactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.
Collapse
Affiliation(s)
- Salvatore M Giampaolo
- Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Fisciano (SA), Italy
| | | | | |
Collapse
|
19
|
Adesso G, Illuminati F. Strong monogamy of bipartite and genuine multipartite entanglement: the Gaussian case. PHYSICAL REVIEW LETTERS 2007; 99:150501. [PMID: 17995148 DOI: 10.1103/physrevlett.99.150501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2007] [Indexed: 05/25/2023]
Abstract
We demonstrate the existence of general constraints on distributed quantum correlations, which impose a trade-off on bipartite and multipartite entanglement at once. For all N-mode Gaussian states under permutation invariance, we establish exactly a monogamy inequality, stronger than the traditional one, that by recursion defines a proper measure of genuine N-partite entanglement. Strong monogamy holds as well for subsystems of arbitrary size, and the emerging multipartite entanglement measure is found to be scale invariant. We unveil its operational connection with the optimal fidelity of continuous variable teleportation networks.
Collapse
Affiliation(s)
- Gerardo Adesso
- Dipartimento di Fisica "E. R. Caianiello," Università degli Studi di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy
| | | |
Collapse
|
20
|
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.
Collapse
Affiliation(s)
- O Legeza
- Research Institute for Solid State Physics and Optics, H-1525, Budapest, Hungary
| | | | | | | |
Collapse
|
21
|
Buonsante P, Vezzani A. Ground-state fidelity and bipartite entanglement in the Bose-Hubbard model. PHYSICAL REVIEW LETTERS 2007; 98:110601. [PMID: 17501037 DOI: 10.1103/physrevlett.98.110601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2007] [Indexed: 05/15/2023]
Abstract
We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.
Collapse
Affiliation(s)
- P Buonsante
- Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
| | | |
Collapse
|
22
|
Osterloh A, Palacios G, Montangero S. Enhancement of pairwise entanglement via Z2 symmetry breaking. PHYSICAL REVIEW LETTERS 2006; 97:257201. [PMID: 17280385 DOI: 10.1103/physrevlett.97.257201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2006] [Indexed: 05/13/2023]
Abstract
We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition. This results in an order-induced enhancement of entanglement, and we report on two examples where this takes place.
Collapse
Affiliation(s)
- Andreas Osterloh
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | | | | |
Collapse
|
23
|
Osborne TJ, Verstraete F. General monogamy inequality for bipartite qubit entanglement. PHYSICAL REVIEW LETTERS 2006; 96:220503. [PMID: 16803293 DOI: 10.1103/physrevlett.96.220503] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2005] [Indexed: 05/10/2023]
Abstract
We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy inequality to the concept of frustration of correlations in quantum spin systems.
Collapse
Affiliation(s)
- Tobias J Osborne
- Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
| | | |
Collapse
|
24
|
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.
Collapse
Affiliation(s)
- O Legeza
- Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary
| | | |
Collapse
|
25
|
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.
Collapse
Affiliation(s)
- Tommaso Roscilde
- Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA
| | | | | | | | | |
Collapse
|
26
|
Hartmann M, Mahler G, Hess O. Local versus global thermal states: correlations and the existence of local temperatures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066148. [PMID: 15697475 DOI: 10.1103/physreve.70.066148] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2004] [Revised: 08/12/2004] [Indexed: 05/24/2023]
Abstract
We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature T . We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of n subsystems each, and when these groups have the same temperature T. While in classical mechanics the validity of this procedure only depends on the size of the groups n, in quantum mechanics the minimum group size n(min) also depends on the temperature T! As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. We discuss various features that show up due to the characteristics of the models considered. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to T-3 below.
Collapse
Affiliation(s)
- Michael Hartmann
- Institute of Technical Physics, DLR Stuttgart, 70569 Stuttgart, Germany.
| | | | | |
Collapse
|