The Quantum Random Energy Model is the Limit of Quantum $ p $-Spin Glasses

TL;DR

This paper proves that as the interaction order p increases, the free energy of quantum p-spin glasses converges to that of the quantum random energy model, linking complex quantum spin systems to a simpler limiting case.

Contribution

It demonstrates the convergence of the free energy of quantum p-spin glasses to the quantum random energy model as p approaches infinity, combining analytical techniques and geometric analysis.

Findings

Convergence of free energy as p → ∞

Connection between quantum p-spin glasses and quantum REM

Insights into classical and quantum free energy properties

Abstract

We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \to \infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy model. This is accomplished by combining existing analytical techniques addressing the non-commutative properties of such quantum glasses, with the description of the typical geometry of extreme negative deviations of the classical $ p $-spin glass. We also review properties of the corresponding classical free energy and conjectures addressing $ 1/p $-corrections in the quantum case.