Solving the Schroedinger equation for the Sherrington-Kirkpatrick model in a transverse field

TL;DR

This paper numerically solves the Schrödinger equation for small systems to accurately identify the quantum critical point and exponents of the infinite-range Ising spin glass in a transverse field at zero temperature.

Contribution

It introduces a numerical method for solving the Schrödinger equation that provides precise estimates of critical parameters in a quantum spin glass model.

Findings

Critical transverse field $\Gamma_c=1.47\pm 0.01$

Critical exponents agree with analytical predictions

Method yields accurate results for small system sizes

Abstract

By numerically solving the Schr\"oedinger equation for small sizes we investigate the quantum critical point of the infinite-range Ising spin glass in a transverse field at zero temperature. Despite its simplicity the method yields accurate information on the value of the critical field and critical exponents. We obtain $\Gamma_c=1.47\pm 0.01$ and check that exponents are in agreement with analytical approaches.