Phase transitions and gaps in quantum random energy models

TL;DR

This paper analyzes quantum random energy models to identify phase transitions and energy gaps, revealing a universal first order quantum phase transition with implications for quantum annealing algorithms.

Contribution

It provides a rigorous characterization of ground and excited states in quantum random energy models, establishing the existence of a universal first order quantum phase transition.

Findings

Existence of a universal first order quantum phase transition.

Exponential vanishing of the minimal energy gap at the transition.

Finite average energy gap over random realizations.

Abstract

By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and continuous. We rigorously establish the existence of a universal first order quantum phase transition, obeyed by both the ground and the first excited states. The presence of an exponentially vanishing minimal gap at the transition is general but, quite interestingly, the gap averaged over the realizations of the random potential is finite. This fact leaves still open the chance for some effective quantum annealing algorithm, not necessarily based on a quantum adiabatic scheme.