Phase diagram of the lattice Wess-Zumino model from rigorous lower bounds on the energy

TL;DR

This paper establishes rigorous lower bounds on the ground state energy density of the 2D lattice N=1 Wess-Zumino model, enabling analysis of phase transitions and symmetry breaking with numerical methods.

Contribution

It introduces a sequence of exact lower bounds on the energy density that converge to the true value, providing a new rigorous approach to studying the model's phase diagram.

Findings

Transition point accurately determined

Bounds agree with Monte Carlo simulations

Method enables rigorous analysis of symmetry breaking

Abstract

We study the lattice N=1 Wess-Zumino model in two dimensions and we construct a sequence $\rho^{(L)}$ of exact lower bounds on its ground state energy density $\rho$, converging to $\rho$ in the limit $L\to\infty$. The bounds $\rho^{(L)}$ can be computed numerically on a finite lattice with $L$ sites and can be exploited to discuss dynamical symmetry breaking. The transition point is determined and compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.