Two-dimensional quantum-link lattice Quantum Electrodynamics at finite density

TL;DR

This paper introduces a tensor network method for simulating two-dimensional lattice gauge theories with fermionic matter at finite density, enabling the study of quantum regimes and phase transitions.

Contribution

It develops an efficient tensor network approach using quantum link and fermionic rishon representations for 2D lattice gauge theories with matter at finite density.

Findings

Successfully simulated 16x16 lattice QED with fermions.

Detected phase separation at different filling densities.

Demonstrated the method's extension to 3D systems.

Abstract

We present an unconstrained tree tensor network approach to the study of lattice gauge theories in two spatial dimensions showing how to perform numerical simulations of theories in presence of fermionic matter and four-body magnetic terms, at zero and finite density, with periodic and open boundary conditions. We exploit the quantum link representation of the gauge fields and demonstrate that a fermionic rishon representation of the quantum links allows us to efficiently handle the fermionic matter while finite densities are naturally enclosed in the tensor network description. We explicit perform calculations for quantum electrodynamics in the spin-one quantum link representation on lattice sizes of up to 16x16 sites, detecting and characterizing different quantum regimes. In particular, at finite density, we detect signatures of a phase separation as a function of the bare mass values at different filling densities. The presented approach can be extended straightforwardly to three spatial dimensions.