Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory

TL;DR

This paper introduces a matrix product variational approach to efficiently identify gauge-invariant states in a Z_2 lattice gauge theory, ensuring Gauss law constraints are satisfied in a ladder chain setup.

Contribution

It presents a novel matrix product ansatz method for gauge-invariant state approximation in Z_2 lattice gauge theories, incorporating Gauss law enforcement.

Findings

Successfully identified low-lying gauge-invariant states

Validated the method through numerical diagonalization

Demonstrated efficiency in enforcing gauge constraints

Abstract

The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. In this work, we propose an efficient variational method based on the matrix product ansatz for a Z_2 lattice gauge theory on a spatial ladder chain. Gauge invariant low-lying states are identified by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian.