Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems

TL;DR

This paper develops a mean-field quantum spin glass theory using path integrals, analyzing phase transitions and quantum fluctuations in the transverse Ising model, with applications to the SK model.

Contribution

It introduces a novel mean-field approach with path integrals and semiclassical analysis for quantum spin glasses, providing detailed phase transition insights.

Findings

Identifies the spin glass-paramagnetic transition point at b3/J 1.62 at T=0

Develops an effective free energy in terms of classical order parameters

Analyzes imaginary-time dependence of order parameters

Abstract

We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several methods such as the semiclassical method and the gauge transformation. As an application we consider the Sherrington-Kirkpatrick model in a transverse field. Using the Landau expansion and its improved versions, we give a detailed analysis of the imaginary-time dependence of the order parameters. Integrating out the quantum part of the order parameters, we obtain the effective renormalized free energy written in terms of the classically defined order parameters. Our method allows us to obtain the spin glass-paramagnetic phase transition point $\Gamma/J\sim 1.62$ at T=0.