arXiv:cond-mat/9706040 · Physical Review Letters

Emergence of Quantum Chaos in Finite Interacting Fermi Systems

Philippe Jacquod, Dima L. Shepelyansky

Published Sep 8, 1997• 215 citations

Abstract

We study the level spacing statistics $P(s)$ in many-body Fermi systems and determine a critical two-body interaction strength ${U}_{c}$ at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level, the results allow one to find a critical temperature ${T}_{\mathrm{ch}}$ above which quantum chaos and thermalization set in.

DOI: 10.1103/physrevlett.79.1837

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arXiv:cond-mat/9706040 · Physical Review Letters

Emergence of Quantum Chaos in Finite Interacting Fermi Systems

Philippe Jacquod, Dima L. Shepelyansky

Published Sep 8, 1997• 215 citations

arXiv HTML PDF

Abstract

We study the level spacing statistics

P(s)

in many-body Fermi systems and determine a critical two-body interaction strength

{U}_{c}

at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level, the results allow one to find a critical temperature

{T}_{\mathrm{ch}}

above which quantum chaos and thermalization set in.

DOI: 10.1103/physrevlett.79.1837

Related papers

Scaling near the quantum chaos border in interacting Fermi systems

Pil Hun Song

The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution $P(s)$ as a function of interaction strength U and the excitation energy $\ensuremath{\epsilon}$ above the Fermi level. As U increases, $P(s)$ undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z=(U{\ensuremath{\epsilon}}^{\ensuremath{\alpha}}\ensuremath{-}{u}_{0}){\ensuremath{\epsilon}}^{1/(2\ensuremath{\nu})},$ where ${u}_{0}$ is a constant. While the exponent $\ensuremath{\alpha},$ which determines the global change of the chaos border, is indecisive within a broad range of $0.9\ensuremath{\sim}2.0,$ the finiteness of $\ensuremath{\nu},$ which comes from the increase of the Fock space size with $\ensuremath{\epsilon},$ suggests that the transition becomes sharp as $\ensuremath{\epsilon}$ increases.The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution $P(s)$ as a function of interaction strength U and the excitation energy $\ensuremath{\epsilon}$ above the Fermi level. As U increases, $P(s)$ undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z=(U{\ensuremath{\epsilon}}^{\ensuremath{\alpha}}\ensuremath{-}{u}_{0}){\ensuremath{\epsilon}}^{1/(2\ensuremath{\nu})},$ where ${u}_{0}$ is a constant. While the exponent $\ensuremath{\alpha},$ which determines the global change of the chaos border, is indecisive within a broad range of $0.9\ensuremath{\sim}2.0,$ the finiteness of $\ensuremath{\nu},$ which comes from the increase of the Fock space size with $\ensuremath{\epsilon},$ suggests that the transition becomes sharp as $\ensuremath{\epsilon}$ increases.

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arXiv:cond-mat/9904229Physical review. B, Condensed matterJun 15, 200019 citations

We study the level spacing statistics

P(s)

in many-body Fermi systems and determine a critical two-body interaction strength

{U}_{c}

at which a crossover from Poisson to Wigner-Dyson statistics takes place. Near the Fermi level, the results allow one to find a critical temperature

{T}_{\mathrm{ch}}

above which quantum chaos and thermalization set in.

The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution

P(s)

as a function of interaction strength U and the excitation energy $\ensuremath{\epsilon}$ above the Fermi level. As U increases,

P(s)

undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z=(U{\ensuremath{\epsilon}}^{\ensuremath{\alpha}}\ensuremath{-}{u}_{0}){\ensuremath{\epsilon}}^{1/(2\ensuremath{\nu})},$ where

{u}_{0}

is a constant. While the exponent $\ensuremath{\alpha},$ which determines the global change of the chaos border, is indecisive within a broad range of $0.9\ensuremath{\sim}2.0,$ the finiteness of $\ensuremath{\nu},$ which comes from the increase of the Fock space size with $\ensuremath{\epsilon},$ suggests that the transition becomes sharp as $\ensuremath{\epsilon}$ increases.

P(s)

statistics takes place. At $U\ensuremath{\ge}{U}_{c}$ the eigenstates are composed of a large number of noninteracting states and even for

U<{U}_{c}

there is a regime where

P(s)

is close to the Poisson distribution but $\ensuremath{\xi}\ensuremath{\gg}1$.

We study the level spacing statistics

P(s)

and eigenstate properties of spinless fermions with Coulomb interaction on a two-dimensional lattice at constant filling factor and various disorder strengths. For the noninteracting localized phase in the limit of large lattice size, Coulomb interaction induces a transition of

P(s)

from the Poisson to the Wigner-Dyson distribution, at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature inside the one-particle insulating phase.