Poisson
                    <i>vs.</i>
                    GOE Statistics in Integrable and Non-Integrable Quantum Hamiltonians

Poilblanc, Didier; Ziman, Timothy; Bellissard, Jean; Mila, Frédéric; Montambaux, Gilles

doi:10.1209/0295-5075/22/7/010

Cited by 158 publications

(142 citation statements)

References 21 publications

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“…For a non-integrable model, the eigenvalues follow a GOE distribution (Gaussian Orthogonal Ensemble) [17]. It can be shown for lattice models which are solvable by the Bethe ansatz that the eigenvalues are Poisson distributed [18].…”

Section: Connection To Integrabilitymentioning

confidence: 99%

Transport properties of one-dimensional Hubbard models

1999

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We present results for the zero and finite temperature Drude weight D(T ) and for the Meissner fraction of the attractive and the repulsive Hubbard model, as well as for the model with next nearest neighbor repulsion. They are based on Quantum Monte Carlo studies and on the Bethe ansatz. We show that the Drude weight is well defined as an extrapolation on the imaginary frequency axis, even for finite temperature. The temperature, filling, and system size dependence of D is obtained. We find counterexamples to a conjectured connection of dissipationless transport and integrability of lattice models.

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Section: Connection To Integrabilitymentioning

confidence: 99%

Transport properties of one-dimensional Hubbard models

1999

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“…These behaviors of the level-spacing distribution have been observed in one-dimensional (1D), 2,3,8 2D, 1,4,7 and 3D 7 spin systems. They are also confirmed for strongly correlated systems, 10 and applied to the recent study of quantum dots.…”

Section: Introductionmentioning

confidence: 66%

“…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%

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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“…As we have extensively discussed, MBL is a special case of integrable system (the reader can find more details on the spectral statistics in Refs. [4,[64][65][66]). In order to distinguish the various phases, instead of considering the whole LSS, we can restrict to a quantity whose average takes markedly different values on the two distributions.…”

Section: Appendix A: Phase Diagrammentioning

confidence: 99%

Signatures of many-body localization in the dynamics of two-site entanglement

et al. 2016

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We are able to detect clear signatures of dephasing -a distinct trait of many-body localisation (MBL) -via the dynamics of two-site entanglement, quantified through the concurrence. Using the protocol implemented by M. Schreiber et al. [Science 349, 842 (2015)], we show that in the MBL phase the average two-site entanglement decays in time as a power law, while in the Anderson localised phase it tends to a plateau. The power-law exponent is not universal and displays a clear dependence on the interaction strength. This behaviour is also qualitatively different from the ergodic phase, where the two-site entanglement decays exponentially. All the results have been obtained by means of time-dependent density matrix renormalisation group simulations, and further corroborated by analytical calculations on an effective model. Two-site entanglement has been already measured in cold atoms: our analysis paves the way for the first direct experimental test of many-body dephasing in the MBL phase.

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Poisson vs. GOE Statistics in Integrable and Non-Integrable Quantum Hamiltonians

Cited by 158 publications

References 21 publications

Transport properties of one-dimensional Hubbard models

Transport properties of one-dimensional Hubbard models

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

Signatures of many-body localization in the dynamics of two-site entanglement

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