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Townsend E, Neuman T, Debrecht A, Aizpurua J, Bryant G. Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains. PHYSICAL REVIEW. B 2021; 103:10.1103/physrevb.103.195429. [PMID: 36452917 PMCID: PMC9706508 DOI: 10.1103/physrevb.103.195429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The exact study of small systems can guide us toward relevant measures for extracting information about many-body physics as we move to larger and more complex systems capable of quantum information processing or quantum analog simulation. We use exact diagonalization to study many electrons in short 1-D atom chains represented by long-range extended Hubbard-like models. We introduce a novel measure, the Single-Particle Excitation Content (SPEC) of an eigenstate and show that the dependence of SPEC on eigenstate number reveals the nature of the ground state (ordered phases), and the onset and saturation of correlation between the electrons as Coulomb interaction strength increases. We use this SPEC behavior to identify five regimes as interaction is increased: a non-interacting single-particle regime, a regime of perturbative Coulomb interaction in which the SPEC is a nearly universal function of eigenstate number, the onset and saturation of correlation, a regime of fully correlated states in which hopping is a perturbation and SPEC is a different universal function of state number, and the regime of no hopping. In particular, the behavior of the SPEC shows that when electron-electron correlation plays a minor role, all of the lowest energy eigenstates are made up primarily of single-particle excitations of the ground state, and as the Coulomb interaction increases, the lowest energy eigenstates increasingly contain many-particle excitations. In addition, the SPEC highlights a fundamental, distinct difference between a non-interacting system and one with minute, very weak interactions. While SPEC is a quantity that can be calculated for small exactly diagonalizable systems, it guides our intuition for larger systems, suggesting the nature of excitations and their distribution in the spectrum. Thus, this function, like correlation functions or order parameters, provides us with a window of intuition about the behavior of a physical system.
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Affiliation(s)
| | - Tomáš Neuman
- Centro de Física de Materiales CFM - MPC, Centro Mixto CSIC-UPV/EHU, 20018 San Sebastián-Donostia, Basque Country, Spain
- Donostia International Physics Center (DIPC), 20018 San Sebastián-Donostia, Basque Country, Spain
- Nanoscale Device Characterization Division and Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423, USA
- University of Maryland, College Park, Maryland 20742, USA
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, 23, rue du Loess 67034, Strasbourg France
| | - Alex Debrecht
- Nanoscale Device Characterization Division and Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423, USA
- University of Maryland, College Park, Maryland 20742, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Javier Aizpurua
- Centro de Física de Materiales CFM - MPC, Centro Mixto CSIC-UPV/EHU, 20018 San Sebastián-Donostia, Basque Country, Spain
- Donostia International Physics Center (DIPC), 20018 San Sebastián-Donostia, Basque Country, Spain
| | - Garnett Bryant
- Nanoscale Device Characterization Division and Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423, USA
- University of Maryland, College Park, Maryland 20742, USA
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Xiang YY, Liu XJ, Yuan YH, Cao J, Tang CM. Doping dependence of the phase diagram in one-dimensional extended Hubbard model: a functional renormalization group study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:125601. [PMID: 30630143 DOI: 10.1088/1361-648x/aafd4d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Using functional renormalization group method, we studied the phase diagram of the one-dimensional extended Hubbard model at different dopings. At half filling, variety of states strongly compete with each other. These states include spin-density wave, charge-density wave, s-wave and p -wave superconductivity, phase separation, and an exotic bond-order wave. By doping, system favours superconductivity more than density waves. At 1/8 doping, a new area of extended s-wave superconductivity emerges between charge density wave and bond-order wave regions. If the system is doped to 1/4-doping, a new area of p -wave superconductivity emerges between charge-density wave and spin-density wave regions.
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Affiliation(s)
- Yuan-Yuan Xiang
- Department of Physics, College of Science, Hohai University, Nanjing, People's Republic of China
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Abstract
We study the connections between local quantum coherence (LQC) based on Wigner-Yanase skew information and quantum phase transitions (QPTs). When applied on the one-dimensional Hubbard, XY spin chain with three-spin interaction, and Su-Schrieffer-Heeger models, the LQC and its derivatives are used successfully to detect different types of QPTs in these spin and fermionic systems. Furthermore, the LQC is effective as the quantum discord (QD) in detecting QPTs at finite temperatures, where the entanglement has lost its effectiveness. We also demonstrate that the LQC can exhibit different behaviors in many forms compared with the QD.
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Kumar M, Topham BJ, Yu R, Ha QBD, Soos ZG. Magnetic susceptibility of alkali-tetracyanoquinodimethane salts and extended Hubbard models with bond order and charge density wave phases. J Chem Phys 2011; 134:234304. [DOI: 10.1063/1.3598952] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mierzejewski M, Łuczka J, Dajka J. Current in Hubbard rings manipulated via magnetic flux. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:245301. [PMID: 21393779 DOI: 10.1088/0953-8984/22/24/245301] [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 currents in a quantum ring threaded by a magnetic flux which is varied in an arbitrary way from an initial constant value φ(1) at time t(1) to a final constant value φ(2) at time t(2). We analyze how the induced currents for t > t(2) can be controlled by the rate of flux variation [Formula: see text]. The dynamics of electrons in the ring is described using the Hubbard and the extended Hubbard models. In the Hubbard model with infinite on-site repulsion the current for t > t(2) is shown to be independent of the flux variation before t(2) and is fully determined by a solution of the initial equilibrium problem and by the value φ(2) of the flux. For intermediate values of the interaction strength the current displays regular or irregular time oscillations and the amplitude of oscillations is sensitive to the rate of the flux changing [Formula: see text]: slow changes of the flux result in small amplitudes of the current oscillations and vice versa. We demonstrate that the time dependence of the induced current bears information on electronic correlations. Our results have important implications for not only mesoscopic rings but also the designing of quantum motors built out of ring-shaped optical lattices.
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Affiliation(s)
- M Mierzejewski
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
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McQueen T, Ho D, Jiménez Cahua C, Cava R, Pascal R, Soos Z. Realization of the bond order wave (BOW) phase of extended Hubbard models in Rb–TCNQ(II). Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2009.04.085] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Ejima S, Nishimoto S. Phase diagram of the one-dimensional half-filled extended Hubbard model. PHYSICAL REVIEW LETTERS 2007; 99:216403. [PMID: 18233235 DOI: 10.1103/physrevlett.99.216403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2007] [Indexed: 05/25/2023]
Abstract
We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).
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Affiliation(s)
- Satoshi Ejima
- Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
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Aligia AA, Anfossi A, Arrachea L, Degli Esposti Boschi C, Dobry AO, Gazza C, Montorsi A, Ortolani F, Torio ME. Incommmensurability and unconventional superconductor to insulator transition in the hubbard model with bond-charge interaction. PHYSICAL REVIEW LETTERS 2007; 99:206401. [PMID: 18233165 DOI: 10.1103/physrevlett.99.206401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2007] [Indexed: 05/25/2023]
Abstract
We determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U>0 at half-filling. For large enough X<t the model shows three phases. For large U the system is in the spin-density wave phase as in the usual Hubbard model. As U decreases, there is first a spin transition to a spontaneously dimerized bond-ordered wave phase and then a charge transition to a novel phase in which the dominant correlations at large distances correspond to an incommensurate singlet superconductor.
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Affiliation(s)
- A A Aligia
- Comisión Nacional de Energía Atómica, Centro Atómico Bariloche and Instituto Balseiro, 8400 S.C. de Bariloche, Argentina
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Tam KM, Tsai SW, Campbell DK. Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model. PHYSICAL REVIEW LETTERS 2006; 96:036408. [PMID: 16486748 DOI: 10.1103/physrevlett.96.036408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2005] [Indexed: 05/06/2023]
Abstract
We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.
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Affiliation(s)
- Ka-Ming Tam
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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