The quantum Almeida-Thouless line in the self-overlap-corrected quantum Sherrington-Kirkpatrick model

TL;DR

This paper analyzes the phase transition boundary in the quantum SK model with self-overlap correction, using a simplified Parisi variational principle involving classical order parameters.

Contribution

It provides a complete analysis of the glass transition in the quantum SK model with a new simplified variational approach.

Findings

Determined the phase boundary between glassy and paramagnetic phases.

Developed a simplified Parisi variational principle for quantum pressure.

Analyzed the pressure of self-overlap-constrained quantum SK and Hopfield models.

Abstract

We present a complete analysis of the glass transition in the self-overlap-corrected Sherrington-Kirkpatrick (SK) model in a transverse magnetic field, also referred to as the quantum SK model. In particular, we determine the phase boundary separating the glassy and paramagnetic phases. The proof is based on a simplified Parisi variational principle for the quantum pressure, which only involves classical Parisi order parameters. As part of the proof, we also analyze the pressure of the self-overlap-constrained quantum SK model and its Parisi description, as well as the pressure of generalized quantum Hopfield models.