4.7 Article

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

Journal

PHYSICAL REVIEW E
Volume 106, Issue 5, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.106.054144

Keywords

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Funding

  1. United States National Science Foundation (NSF) [DMR-1936006]
  2. Kreitman School of Advanced Graduate Studies at Ben-Gurion University
  3. MPS Simons Foundation [678586]

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This article studies the applications of extreme-value distributions in various contexts, with a focus on the ground-state energy distribution of disordered many-body quantum systems. An analytical expression is derived that accurately describes the ground-state energy distribution of the systems, reproducing Tracy-Widom distribution for some models but showing discrepancies for others. The analytical expression captures all of these distributions, playing a similar role as the Brody distribution does for the bulk of the spectrum.
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.

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