Truncated eigenvalue equation and long wavelength behavior of lattice gauge theory

TL;DR

This paper introduces a new truncation method for Hamiltonian lattice gauge theory that efficiently approaches continuum physics, demonstrating rapid convergence and reliable results in lower-dimensional models.

Contribution

The authors present a novel truncation scheme that preserves the continuum limit, enabling direct and efficient analysis of lattice gauge theories.

Findings

Rapid convergence to Monte Carlo data

Effective long wavelength vacuum wave functions

Accurate mass gap predictions at low truncation orders

Abstract

We review our new method, which might be the most direct and efficient way for approaching the continuum physics from Hamiltonian lattice gauge theory. It consists of solving the eigenvalue equation with a truncation scheme preserving the continuum limit. The efficiency has been confirmed by the observations of the scaling behaviors for the long wavelength vacuum wave functions and mass gaps in (2+1)-dimensional models and (1+1)-dimensional $\sigma$ model even at very low truncation orders. Most of these results show rapid convergence to the available Monte Carlo data, ensuring the reliability of our method.