Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks

TL;DR

This paper demonstrates the use of tensor network methods to simulate three-dimensional lattice gauge theories with dynamical matter at finite density, overcoming the sign problem and exploring phase structures and confinement phenomena.

Contribution

It introduces a sign-problem-free tensor network approach for simulating 3D lattice gauge theories with matter at finite density, enabling new non-perturbative insights.

Findings

Identification of collective phases in the model

Observation of a confining phase at large gauge coupling

Analysis of charge-screening effects

Abstract

Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.