Thermal states of random quantum many-body systems

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.

5 pages, 4 figures

References in corpus (4)

• Black holes as mirrors: quantum information in random subsystems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Comment on the paper "Random Quantum Circuits are Approximate 2-designs"
• Diagonal quantum circuits: their computational power and applications

Cited by in corpus (1)

• Particle Diagrams and Statistics of Many-Body Random Potentials