Spectral statistics of the k-body random-interaction model

Abstract

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.

17 pages, no figures

References in corpus (2)

• Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons
• Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

Cited by in corpus (12)

• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Semiclassical roots of universality in many-body quantum chaos
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Origin of chaos in the spherical nuclear shell model: role of symmetries
• Random Matrix Ensembles For Many-Body Quantum Systems
• A smooth transition towards a Tracy-Widom distribution for the largest eigenvalue of interacting $k$-body fermionic Embedded Gaussian Ensembles
• Chaos in fermionic many-body systems and the metal-insulator transition
• Particle diagrams and embedded many-body random matrix theory
• Bivariate moments of the two-point correlation function for embedded Gaussian unitary ensemble with $k$-body interactions
• On the Unification of Random Matrix Theories