String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory

TL;DR

This paper introduces a string-net based regularization of lattice Yang-Mills theories using quantum groups, enabling quantum simulations and revealing quantum scars in nonabelian gauge theories.

Contribution

It develops a $q$-deformed string-net regularization for lattice Yang-Mills theories, facilitating quantum simulation and analysis of quantum scars in nonabelian gauge systems.

Findings

Quantum scars from zero modes exist in nonabelian gauge theories.

The spectrum of single-plaquette models shows cutoff dependence.

The regularization respects nonabelian gauge symmetry via quantum groups.

Abstract

We study the Hamiltonian lattice Yang-Mills theory based on spin networks that provide a useful basis to represent the physical states satisfying the Gauss law constraints. We focus on $\mathrm{SU}(2)$ Yang-Mills theory in $(2+1)$ dimensions. Following the string-net model, we introduce a regularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theory based on the $q$ deformation, which respects the (discretized) $\mathrm{SU}(2)$ gauge symmetry as quantum group, i.e., $\mathrm{SU}(2)_k$, and enables implementation of the lattice Yang-Mills theory both in classical and quantum algorithms by referring to those of the string-net model. Using the regularized Hamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scars are nonthermal energy eigenstates arising in the constrained quantum many-body systems. We find that quantum scars from zero modes, which have been found in abelian gauge theories arise even in a nonabelian gauge theory. We also show the spectrum of a single-plaquette model for SU(2)$_k$ and SU(3)$_k$ with naive cutoff and that based on the $q$-deformation to discuss cutoff dependence of the formulation.