Phase Transition in the Density of States of Quantum Spin Glasses
Abstract
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 Keating et al. (2014) 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 puniform hypergraphs that correspond to pspin glass Hamiltonians acting on n distinguishable spin 1/2 particles. At the critical threshold p = n ^{1/2} we find a sharp classicalquantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory.
 Publication:

Mathematical Physics, Analysis and Geometry
 Pub Date:
 December 2014
 DOI:
 10.1007/s1104001491643
 arXiv:
 arXiv:1407.1552
 Bibcode:
 2014MPAG...17..441E
 Keywords:

 Mathematical Physics;
 Mathematics  Probability;
 15A52;
 82D30
 EPrint:
 21 pages, 2 figures