Supersymmetric Quantum Spherical Spins with Short-Range Interactions

TL;DR

This paper investigates a supersymmetric quantum spherical spin system with short-range interactions, analyzing its critical behavior at zero and finite temperatures, and establishing connections with supersymmetric sigma models.

Contribution

It introduces a supersymmetric quantum spherical spin model with short-range interactions, analyzing its phase transitions, critical exponents, and relation to supersymmetric sigma models.

Findings

Quantum phase transition at zero temperature without supersymmetry breaking

Finite temperature thermal phase transition with broken supersymmetry

Dynamical critical exponent z=2

Abstract

This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent $z=2$. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric $O(N)$ nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large $N$ limit.