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

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.

Theorems & Definitions (10)

• Proposition 1.1: cf. Talagrand:2000aaBovier:2002aaPanchenko:2014aa
• Theorem 1.2
• Proposition 2.1: cf. Lemma 2.1 in MW20
• proof
• Definition 2.2
• Lemma 2.3
• proof
• Lemma 2.4
• proof
• proof : Proof of Theorem \ref{['thm:main']}