Many-body spectral statistics of interacting fermions

Pascaud, M.; Montambaux, Gilles

doi:10.1002/(sici)1521-3889(199811)7:5/6<406::aid-andp406>3.0.co;2-d

Ann. Phys.

1998

DOI: 10.1002/(sici)1521-3889(199811)7:5/6<406::aid-andp406>3.0.co;2-d

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Many-body spectral statistics of interacting fermions

M. Pascaud

Gilles Montambaux

Abstract: We h a ve studied the appearance of chaos in the many-body spectrum of interacting Fermions. The coupling of a single state to the Fermi sea is considered. This state is coupled to a hierarchy of states corresponding to one or several particle-hole excitations. We h a ve considered various couplings between two successive generations of this hierarchy and determined under which conditions this coupling can lead to Wigner-Dyson correlations. We h a ve found that the cross-over from a Poisson to a Wigner distrib… Show more

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Cited by 11 publications

(15 citation statements)

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“…This distinction is blurred as the interactions become stronger and P (S i ) for any i approaches the GOE distribution. This is in agreement with the observations for the distribution of interacting MBE [36][37][38][39][40][41] which show a transition to GOE statistics as interactions become stronger. Thus, it seems that the Li and Haldane conjecture holds even for the ES of interacting systems.…”

supporting

confidence: 92%

Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Leiman¹,

Eisenbach²,

Berkovits³

2015

EPL

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Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane's conjecture on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. In order to demonstrate the correspondence we develope a computational efficient way to calculate the ES of low-excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation structure. The low-lying shell are robust and survive even for strong electronelectron interactions.

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supporting

confidence: 92%

Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Leiman¹,

Eisenbach²,

Berkovits³

2015

EPL

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“…The EE distribution changes from a Gaussian in the metallic regime to a very asymmetric Lévy alpha stable distribution with "fat tails" in the superconducting regime. The ES level spacing (ESLS) distribution fits the Gaussian orthogonal distribution (GOE) expected from interacting many particle system [8,9,[25][26][27][28][29][30] in the metallic regime, while it changes to a Gaussian unitary distribution (GUE) associated with superconducting excitations [31,32] in the superconducting regime. Thus, the EE and ESLS distributions are able to characterize the phase of the system, where other methods fail.…”

mentioning

confidence: 99%

Entanglement Properties and Quantum Phases for a Fermionic Disordered One-Dimensional Wire with Attractive Interactions

Berkovits

2015

Phys. Rev. Lett.

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A fermionic disordered one-dimensional wire in the presence of attractive interactions is known to have two distinct phases, a localized and superconducting, depending on the strength of interaction and disorder. The localized region may also exhibit a metallic behavior if the system size is shorter than the localization length. Here we show that the superconducting phase has a distribution of the entanglement entropy distinct from the metallic regime. The entanglement entropy distribution is strongly asymmetric with a Lévy α-stable distribution (compared to the Gaussian metallic distribution), as is seen also for the second Rényi entropy distribution. Thus, entanglement properties may reveal properties which cannot be detected by other methods.

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“…A detailed numerical investigation of several statistical properties of the type of models can be found also in [2,3,4].…”

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confidence: 99%

Comment on “Models of intermediate spectral statistics”

2001

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In [1] it was proposed, that the nearest-neighbor distribution P (s) of the spectrum of the Bohr-Mottelson model is similar to the semi-Poisson distribution. We show however, that P (s) of this model differs considerably in many aspects from semi-Poisson. In addition we give an asymptotic formula for P (s) as s → 0, which gives P ′ (0) = π √ 3/2 for the slope at s = 0. This is different not only from the GOE case but also from the semi-Poisson prediction that leads to P ′ (0) = 4The motivation for this comment stems from the impression, that the article "models of intermediate spectral statistics" can easily be misinterpreted in two ways: One might be led to believe that (i) the semi-Poisson distribution is universal, and (ii) the universality class of "intermediate statistics" is as well defined and established as for example the Poisson ensemble or the GOE. In this comment, we will argue, that both statements are wrong.The purpose of [1] is to present models which could constitute a "third" universality class of systems which show so called "intermediate statistics", previously introduced by Shklovskii in [5]. The Poissonian and the Gaussian ensemble (for definiteness, consider orthogonal ensembles only) are considered as the first two universality classes in this list.As in the Poissonian and in the GOE case, where the respective members have common and unique statistical properties, one would expect the same to hold for the models with intermediate statistics. In [1] the authors concentrate on the distribution of nearest neighbor spacings. In the Poissonian case it is given by P (s) = exp(−s), in the GOE case it is close to the well known Wigner surmise P (s) ≈ (π/2) exp(−π/4s 2 ), whereas in the case of the "intermediate statistics

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Many-body spectral statistics of interacting fermions

Cited by 11 publications

References 16 publications

Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems

Entanglement Properties and Quantum Phases for a Fermionic Disordered One-Dimensional Wire with Attractive Interactions

Comment on “Models of intermediate spectral statistics”

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