Phase Transition in the Density of States of Quantum Spin Glasses

Understand

We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges.

• This extends the recent results of [6] that were proved for graphs with bounded chromatic number and with symmetric coupling distribution.
• Furthermore, we generalise the result to arbitrary hypergraphs.
• We test the optimality of our condition on the maximal degree for $p$-uniform hypergraphs that correspond to $p$-spin glass Hamiltonians acting on $n$ distinguishable spin-$1/2$ particles.