The Hubbard model at finite chemical potential is a cornerstone for understanding doped correlated systems, but simulations are severely limited by the sign problem. In the auxiliary-field formulation, the spin basis mitigates the sign problem, yet severe ergodicity issues have limited its use. We extend recent advances with normalizing flows at half-filling to finite chemical potential by introducing an annealing scheme enabling ergodic sampling. Compared to state-of-the-art hybrid Monte Carlo in the charge basis, our approach accurately reproduces exact diagonalization results while reducing statistical uncertainties by an order of magnitude, opening a new path for simulations of doped correlated systems.
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References (9)
04Divergence Measures and Message Passing , Technical Report2005
05in this formulation is not removed away from half-filling. To demonstrate that our annealing-based NF method can nevertheless model this challenging distribution, we
06Hubbard model is lifted away from half-filling [23].However
07Appendix A: Two-site model distribution —The formal ergodicity problem in the charge basis formulation of the
08Note that we could have equivalently defined the chemical potential term on the diagonal of the hopping matrix
09The relation between fermion matrices at finite chemical potential and the emergence of a sign problem is derived in App. D