Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response

TL;DR

This paper demonstrates that Wilson fermions in (2+1)D lattice QED enable topological phases with nonzero Chern numbers, providing a foundation for quantum simulation of topological phenomena in lattice gauge theories.

Contribution

It systematically analyzes fermion discretization effects, showing Wilson fermions allow topological regimes, and develops gauge-invariant diagnostics for topological response in lattice QED.

Findings

Wilson fermions enable topological phases with nonzero Chern numbers

Two-flavor extension enriches topological structures at finite chemical potential

Gauge-invariant diagnostics effectively probe topological responses

Abstract

The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry, which forbids the emergence of nontrivial topological phases and has led to confusion in the existing literature. In this work, we resolve this obstacle by systematically analyzing fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law. We show that Wilson fermions, already in the minimal one-flavor theory, naturally enable topological regimes with nonzero Chern numbers, and that the two-flavor extension at finite chemical potential further enriches the accessible topological structure. We develop gauge-invariant diagnostics of topological response, including many-body Chern numbers and current correlators that remain robust probes at weak coupling. Finally, through extensive exact diagonalization calculations across both flavor settings, we characterize the spectrum, correlators, and topological invariants, providing a concrete foundation for near-term quantum simulations of topological phases in lattice field theories. The implications of this work for quantum simulations of lattice field theory are analyzed in a joint submission [1].