Tensor-network toolbox for probing dynamics of non-Abelian gauge theories

TL;DR

This paper introduces a tensor-network toolbox for simulating non-Abelian gauge theories, specifically SU(2), using matrix-product states, enabling the study of their dynamics and static properties in one spatial dimension.

Contribution

It develops and benchmarks a matrix-product-state ansatz for SU(2) lattice gauge theory using the loop-string-hadron formulation, applicable to various gauge groups and boundary conditions.

Findings

Successfully computed static observables in SU(2) (1+1)D.

Demonstrated progress in dynamical simulations of non-Abelian gauge theories.

Extended the boundary of existing tensor-network studies in gauge theories.

Abstract

Tensor-network methods enable probing dynamics of strongly interacting quantum many-body systems, including gauge theories, via Hamiltonian simulation, hence bypassing sign problems. They also have the potential to inform efficient quantum-simulation algorithms of the same theories. We develop and benchmark a matrix-product-state ansatz for the SU(2) lattice gauge theory using the loop-string-hadron formulation. This formulation has been demonstrated to be advantageous in Hamiltonian simulation of non-Abelian gauge theories. It is applicable to both SU(2) and SU(3) gauge groups, to periodic and open boundary conditions, and to 1+1 and higher dimensions. In this work, we report on progress in computing static and dynamical observables in a SU(2) gauge theory in (1+1)D, pushing the boundary of existing studies.