Ground-state energy distribution of disordered many-body quantum 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 all the systems that we consider. For several models with short- and long-range random couplings, the ground-state distribution agrees remarkably well with the Tracy-Widom distribution obtained from random matrices. They include transverse Ising models, the Sachdev-Ye model and variants, and a randomized version of the PXP model. In contrast, shapes at odds with the Tracy-Widom distribution are observed for disordered Bose-Hubbard models and the disordered spin-1/2 Heisenberg chain used to investigate many-body localization.