Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble

In this work, we present a new recursive approach for performing Auxiliary Field Quantum Monte Carlo (AFQMC) in the canonical ensemble (CE) that does not require knowledge of chemical potentials. Unlike previous CE algorithms, which relied upon projecting CE properties out from grand canonical simulations, our formalism eliminates the costly need to scan through chemical potentials to fix average particle numbers, enabling efficient and more accurate treatments for systems with fixed particle numbers. To derive this approach, we exploit the fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms will motivate other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the CE.