Chemical Potential and Analytic Continuation for Non-Hermitian Lattice Fermions

Abstract

We introduce a chemical potential for non-Hermitian lattice fermions and show that, for even flavors with degenerate masses and paired chemical potentials $(μ,-μ)$ or $(iμ,iμ)$, the Hybrid Monte Carlo algorithm is free of the sign problem. For one-dimensional free fermions, we demonstrate that the sign problem is a numerical rather than physical obstruction and derive the exact propagator, which is analytic at finite lattice spacing away from its poles but becomes non-analytic in the continuum limit. Finally, we use AI-assisted fitting to perform analytic continuation from imaginary to real chemical potentials.