Matrix product variational formulation for lattice gauge theory

TL;DR

This paper introduces a matrix product variational approach inspired by DMRG for lattice gauge theories, enabling efficient computation of ground states in complex quantum models.

Contribution

It develops a novel matrix product ansatz for Hamiltonian lattice gauge theories, extending DMRG techniques to these systems.

Findings

Successfully describes the S=1/2 Heisenberg chain

Applied to 2D Heisenberg and U(1) plaquette models

Provides a computationally feasible method for vacuum states

Abstract

For hamiltonian lattice gauge theory, we introduce the matrix product anzats inspired from density matrix renormalization group. In this method, wavefunction of the target state is assumed to be a product of finite matrices. As a result, the energy becomes a simple function of the matrices, which can be evaluated using a computer. The minimum of the energy function corresponds to the vacuum state. We show that the S=1/2 Heisenberg chain model are well described with the ansatz. The method is also applied to the two-dimensional S=1/2 Heisenberg and U(1) plaquette chain models.