Two-dimensional quantum spin Hamiltonians: Spectral properties

Pals, P. van Ede van der; Gaspard, Pierre

doi:10.1103/physreve.49.79

Cited by 29 publications

(21 citation statements)

References 11 publications

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“…However, we shall show that it is practically effective for finite-size quantum systems. In fact, the above conjecture has been numerically confirmed for many quantum spin systems such as correlated spin systems [1][2][3][4][5][6][7] and disordered spin systems. [8][9][10][11][12] In the Anderson model of disordered systems, P Poi (s) and P Wig (s) characterize the localized and the metallic phases, respectively.…”

Section: Introductionmentioning

confidence: 72%

Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects

Kudo

Deguchi

2005

J. Phys. Soc. Jpn.

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Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and the XXZ anisotropy, which should reflect competition among quantum chaos, integrability and finite-size effects. Here discrete symmetries play a central role in our analysis. Evaluating the level-spacing distribution, the spectral rigidity and the number variance, we confirm the correspondence between nonintegrability and Wigner behavior in the spectrum. We also show that non-Wigner behavior appears due to mixed symmetries and finite-size effects in some nonintegrable cases.

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Section: Introductionmentioning

confidence: 72%

Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects

Kudo

Deguchi

2005

J. Phys. Soc. Jpn.

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“…More generally, even non-integrable models without apparent classical limits, such as spin systems, can also show such features [3,4]. In contrast, integrable systems generally follow Poisson statistics, which are devoid of level repulsion [5].…”

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confidence: 99%

Universal Scaling of Spectral Fluctuation Transitions for Interacting Chaotic Systems

et al. 2016

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The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random matrix ensemble modeling this dynamical symmetry breaking transition which turns out to be universal and depends on a single scaling parameter only. Coupled kicked rotors, a dynamical systems paradigm for such transitions, are compared with this ensemble and excellent agreement is found for the nearest-neighbor-spacing distribution. It turns out that this transition is described quite accurately using perturbation theory.Quantization of fully chaotic systems is known to lead to the spectral fluctuations of random matrix theory (RMT) [1] and to exhibit energy level repulsion [2]. More generally, even non-integrable models without apparent classical limits, such as spin systems, can also show such features [3,4]. In contrast, integrable systems generally follow Poisson statistics, which are devoid of level repulsion [5]. It is also well understood that combining spectra of different irreducible representations tends toward Poisson statistics in the limit of superposing many sequences [6,7]. An instance where this occurs is for the spectra of two separable, but individually chaotic systems. Whereas each subsystem possesses RMT fluctuations, the full spectrum tends to Poisson fluctuations in the large dimensionality limit [8].This begs the question of what happens to spectral fluctuations if such separable, but quantum chaotic subsystems, interact. There are many motivations for studying such systems. For example, they may be of direct physical interest, such as conduction electrons in chaotic quantum dots interacting through a screened Coulomb potential [9]. Another motivation derives from quantum information theory where the development of entanglement is of particular importance [10]. Two quantum spin chains with RMT spectral fluctuations coupled in a ladder configuration is a many-body situation where such transitions are possible as well.Typically, the interaction between two subsystems leads to entanglement and paves the way for RMT fluctuations of the combined system. This Poisson-to-RMT transition can be viewed as a dynamical symmetry breaking in analogy to fundamental symmetry breaking; the first exact RMT solution to a symmetry breaking problem involved time-reversal invariance [11]. For modeling a particular dynamical system, it is important to connect dynamical system parameters with the abstract transi- There are a couple of other possible cases of a Poissonto-RMT transition, a metal-insulator transition where states transition from localized to extended [14], and the perturbation of an integrable dynamical system [12,15] that renders it chaotic for sufficient perturbation strength. In neither of these possibilities is there a simple globally coupled Poisson-to-RMT ensemble. Various complications, such as the metal-insulator transition, the KAM theorem regarding the surviv...

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“…1,2,3,4,5,6,7,8,9 If a given Hamiltonian is integrable by the Bethe ansatz, the level-spacing distribution should be described by the Poisson distribution:…”

Section: Introductionmentioning

confidence: 99%

“…The numerical observations 1,2,3,4,7,8,10,11 are important. In fact, for the quantum spin systems, there has been no theoretical or analytical derivation of the suggested behaviors of the level-spacing distribution.…”

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confidence: 99%

Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupledXXZspin chains

Kudo

Deguchi

2003

Phys. Rev. B

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The level-spacing distributions of XXZ spin chains with next-nearest-neighbor couplings are studied under periodic boundary conditions. We confirm that integrable XXZ spin chains mostly have the Poisson distribution as expected. On the contrary, the level-spacing distributions of next-nearestneighbor coupled XXZ chains are given by non-Wigner distributions. It is against the expectations, since the models are nonintegrable.

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Two-dimensional quantum spin Hamiltonians: Spectral properties

Cited by 29 publications

References 11 publications

Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects

Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects

Universal Scaling of Spectral Fluctuation Transitions for Interacting Chaotic Systems

Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupledXXZspin chains

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