Speaker
Description
Auxiliary-field quantum Monte Carlo methods provide a powerful route to unbiased simulations of strongly correlated quantum systems. While determinant quantum Monte Carlo has been highly successful, its standard formulation is naturally adapted to particle-number-conserving Hamiltonians. Pfaffian quantum Monte Carlo extends this framework to systems, that do not conserve particle number.
Existing implementations of Pfaffian quantum Monte Carlo have largely followed the BSS approach. In this talk, I will present the construction of an efficient Hybrid Monte Carlo (HMC) formulation of Pfaffian quantum Monte Carlo, bringing the advantages of HMC sampling to a broader class of fermionic systems. The central idea is to adapt the efficient matrix-product routines used in HMC formulations of determinant quantum Monte Carlo to the Pfaffian formulation, while preserving the same computational asymptotic scaling.
Because Pfaffian quantum Monte Carlo is naturally formulated in the Majorana basis, additional Hubbard–Stratonovich decoupling channels become available, which can in some cases alleviate or remove the sign problem. The resulting interactions, however, can be non-diagonal and often lack simple closed-form force terms. I will present a method to circumvent this difficulty by approximating the gradient without introducing any systematic errors into the observables.