Ground-state energy distribution of disordered many-body quantum systems

TL;DR

This paper derives an analytical expression for the ground-state energy distribution in disordered many-body quantum systems, accurately capturing various models including Tracy-Widom and others, aiding understanding of low-energy properties.

Contribution

It introduces a universal analytical formula for ground-state energy distributions that applies across different disordered quantum models, unifying their statistical descriptions.

Findings

The formula reproduces Tracy-Widom distribution for certain models.

It accurately describes distributions for Bose-Hubbard and Heisenberg models.

The approach unifies ground-state energy statistics across diverse disordered systems.

Abstract

Extreme-value distributions are studied in the context of a broad range of problems, from the equilibrium properties of low-temperature disordered systems to the occurrence of natural disasters. Our focus here is on the ground-state energy distribution of disordered many-body quantum systems. We derive an analytical expression that, upon tuning a parameter, reproduces with high accuracy the ground-state energy distribution of the systems that we consider. For some models, it agrees with the Tracy-Widom distribution obtained from Gaussian random matrices. They include transverse Ising models, the Sachdev-Ye model, and a randomized version of the PXP model. For other systems, such as Bose-Hubbard models with random couplings and the disordered spin-1/2 Heisenberg chain used to investigate many-body localization, the shapes are at odds with the Tracy-Widom distribution. Our analytical expression captures all of these distributions, thus playing a role to the lowest energy level similar to that played by the Brody distribution to the bulk of the spectrum.