Phase transitions and gaps in quantum random energy models

Carlo Presilla and Massimo Ostilli

Physica A: Statistical Mechanics and its Applications, 2019, vol. 515, issue C, 57-64

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.

Keywords: Quantum phase transitions; Random energy models; Quantum annealing; Quantum adiabatic theorem (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:515:y:2019:i:c:p:57-64

DOI: 10.1016/j.physa.2018.09.193

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