Thermal states of random quantum many-body systems

TL;DR

This paper investigates the properties of thermal states in random quantum many-body systems, demonstrating how they approach unitary designs at certain temperatures and providing evidence for a phase transition at finite temperature.

Contribution

It introduces a detailed analysis of thermal state ensembles in random Hamiltonians, revealing their convergence to unitary designs and phase transition behavior.

Findings

Thermal states approach unitary t-designs at temperature O(1/ log t).

Local random interactions lead to ensemble achieving a 1-design.

Numerical evidence suggests a phase transition at finite temperature.

Abstract

We study a distribution of thermal states given by random Hamiltonians with a local structure. We show that the ensemble of thermal states monotonically approaches the unitarily invariant ensemble with decreasing temperature if all particles interact according to a single random interaction and achieves a state $t$-design at temperature $O(1/\log(t))$. For the system where the random interactions are local, we show that the ensemble achieves a state $1$-design. We then provide numerical evidence indicating that the ensemble undergoes a phase transition at finite temperature.