U(1) flux tube profiles from Hamiltonian lattice gauge theory using a random walk ground-state projector

TL;DR

This paper introduces a novel method using a self-guided random walk to efficiently compute the ground-state electric field distribution in 2+1 dimensional U(1) lattice gauge theory, providing a new approach to studying flux tubes.

Contribution

It presents a new random walk-based technique for solving the ground-state problem in Hamiltonian lattice gauge theory, focusing on electric field distributions in the string sector.

Findings

Efficient measurement of electric field distributions using the new method.

Application of the method to U(1) gauge theory in 2+1 dimensions.

Potential for improved understanding of flux tube profiles.

Abstract

We use a self-guided random walk to solve the ground-state problem of Hamiltonian U(1) pure gauge theory in 2+1 dimensions in the string sector. By making use of the electric-field representation, we argue that the spatial distribution of the electric field can be more easily measured than in ordinary Monte Carlo simulations.