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Original version
Nakata, Y.; Osborne, T. J.: Thermal states of random quantum many-body systems. In: Physical Review A 90 (2014), Nr. 5, 50304. DOI: https://doi.org/10.1103/PhysRevA.90.050304
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.
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