Gauge invariance in a Z_2 hamiltonian lattice gauge theory

TL;DR

This paper introduces a matrix product variational method for Z_2 lattice gauge theory, effectively identifying gauge-invariant states and capturing phase transitions on ladder and square lattices.

Contribution

It presents a novel variational approach using matrix product states for Z_2 lattice gauge theories, ensuring gauge invariance and accurately modeling phase transitions.

Findings

Successfully identifies gauge-invariant low-lying states.

Reproduces the second order phase transition on the square lattice.

Demonstrates efficiency of the variational method for different lattice geometries.

Abstract

We propose an efficient variational method for $Z_2$ lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.