Applying the Worldvolume Hybrid Monte Carlo method to the Hubbard model away from half filling

Abstract: The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient and low-cost algorithm for addressing the sign problem. It mitigates the sign problem while avoiding the ergodicity issues that are intrinsic to algorithms based on Lefschetz thimbles. In this study, we apply the WV-HMC method to the Hubbard model away from half filling, which is known to suffer from a severe sign problem. We compute the number density on lattices of spatial size $6 \times 6$ and $8 \times 8$ at inverse temperature $\beta = 6.4$ using $N_t = 20$ Trotter steps. Our results show that the WV-HMC method remains effective even in parameter regions where non-thimble Monte Carlo methods fail due to severe sign problems. In this work, we employ direct solvers for fermion matrix inversion, with a computational cost of $O(N^3)$, where $N$ is the number of degrees of freedom and proportional to the spacetime lattice volume. An alternative algorithm employing pseudofermions and iterative solvers, which reduces the cost to $O(N^2)$ at the expense of careful parameter tuning, will be discussed in a separate publication.