Chaos in fermionic many-body systems and the metal-insulator transition

Abstract

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix ensemble ScE that mimics that transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.

8 figures, 8 pages, amplified and corrected, main conclusion unchanged

References in corpus (4)

• Anderson Transitions
• Periodic-Orbit Theory of Level Correlations
• Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices
• On the problem of many-body localization

Cited by in corpus (6)

• Average-fluctuation separation in energy levels in many-particle quantum systems with $k$-body interactions using $q$-Hermite polynomials
• Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition
• 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
• Particle diagrams and embedded many-body random matrix theory
• Level number variance and spectral compressibility in a critical two-dimensional random matrix model