Intrinsic sign problem for ancillary field Quantum Monte Carlo and a possible remedy

Quantum Monte Carlo (QMC) is a central tool for studying strongly correlated quantum matter. Recent no-go results tie intrinsic sign problems to topological data, implying that certain topologically ordered ground states cannot arise from any stoquastic Hamiltonian, a sufficient condition for sign-free Stochastic Series Expansion (SSE) simulations. Here, we extend the notion of an intrinsic sign problem to auxiliary-field QMC (AFQMC) and prove that topologically ordered phases exhibit the same intrinsic obstruction in AFQMC, without appealing to the existence of a stoquastic parent Hamiltonian. Building on this result, we introduce a two-replica construction that certifies the existence of a sign-free basis for QMC and present a practical algorithm that searches for such a basis.