Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update

Abstract

Ground-state auxiliary-field quantum Monte Carlo (AFQMC) methods have become key numerical tools for studying quantum phases and phase transitions in interacting many-fermion systems. Despite the broad applicability, the efficiency of these algorithms is often limited by the bottleneck associated with the {\it local update} of the field configuration. In this work, we propose two novel update schemes, the {\it delayed update} and {\it block force-bias update}, both of which can generally and efficiently accelerate ground-state AFQMC simulations. The {\it delayed update}, with a predetermined delay rank, is an elegantly improved version of the {\it local update}, accelerating the process by replacing multiple vector-vector outer products in the latter with a single matrix-matrix multiplication. The {\it block force-bias update} is a block variant of the conventional force-bias update, which is a highly efficient scheme for dilute systems but suffers from the low acceptance ratio in lattice models. Our modified scheme maintains the high efficiency while offering flexible tuning of the acceptance ratio, controlled by the block size, for any desired fermion filling. We apply these two update schemes to both the standard and spin-orbit coupled two-dimensional Hubbard models, demonstrating their speedup over the {\it local update} with respect to the delay rank and block size. We also explore their efficiencies across varying system sizes and model parameters. Our results identify a speedup of $\sim$$8$ for systems with $\sim$$1600$ lattice sites. Furthermore, we have investigated the broader applications as well as an application diagram of these update schemes to general correlated fermion systems.