Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states

TL;DR

This paper introduces a new explicit formulation for (1+1)-D SU(2) lattice gauge theory that simplifies the gauge degrees of freedom, enabling efficient spectral analysis with matrix product states and potential quantum simulation applications.

Contribution

It presents a general physical subspace formulation that integrates out gauge fields, facilitating numerical and quantum simulation approaches for the model.

Findings

Determined scaling exponents for the vector mass.

Computed entanglement entropy and its continuum limit scaling.

Analyzed the impact of gauge degree truncation on spectral properties.

Abstract

We propose an explicit formulation of the physical subspace for a (1+1)-dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.