For a one-dimensional free non-Hermitian lattice fermion, the finite-lattice propagator is analytic in the chemical potential, the infinite-volume/continuum limit can destroy that analyticity, and paired potentials (μ,-μ) or (iμ,iμ) make Hybrid Monte Carlo sign-problem-free.
Methods of contemporary gauge theory,
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Chemical Potential and Analytic Continuation for Non-Hermitian Lattice Fermions
For a one-dimensional free non-Hermitian lattice fermion, the finite-lattice propagator is analytic in the chemical potential, the infinite-volume/continuum limit can destroy that analyticity, and paired potentials (μ,-μ) or (iμ,iμ) make Hybrid Monte Carlo sign-problem-free.