Simple Hamiltonian for Quantum Simulation of Strongly Coupled 2+1D SU(2) Lattice Gauge Theory on a Honeycomb Lattice

TL;DR

This paper introduces a simplified spin Hamiltonian that accurately models the physical states of a 2+1D SU(2) lattice gauge theory on a honeycomb lattice, with electric field truncation, facilitating quantum simulations.

Contribution

It presents a novel, simplified Hamiltonian with local Pauli matrix interactions that fully incorporates Gauss's law constraints for the specified gauge theory.

Findings

Hamiltonian accurately describes physical states.

Contains only local Pauli interactions.

Gauss's law fully integrated.

Abstract

We find a simple spin Hamiltonian to describe physical states of $2+1$ dimensional SU(2) lattice gauge theory on a honeycomb lattice with a truncation of the electric field representation at $j_{\rm max}=\frac{1}{2}$. The simple spin Hamiltonian only contains local products of Pauli matrices, even though Gauss's law has been completely integrated out.