Applying the Worldvolume Hybrid Monte Carlo method to the finite-density complex φ⁴ model and the Hubbard model

The sign problem has been a major obstacle to first-principles calculations of important physical systems based on the Markov chain Monte Carlo algorithms. The Worldvolume Hybrid Monte Carlo method~{Fukuma:2020fez} is an efficient and low-cost algorithm to tame the sign problem that also eliminates the ergodicity problem inherent in algorithms based on Lefschetz thimbles. We apply the method to the complex φ⁴ model at finite density as well as to the Hubbard model away from half filling. For the finite-density φ⁴ model, we confirm that the computational cost is of O(N¹) when using linear solvers such as BiCGStab (N: degrees of freedom), in contrast to the O(N³) cost of preceding Lefschetz thimble methods. For the Hubbard model, the computational cost increases due to the presence of the fermion determinant, but we argue that the cost will not exceed O(N²) with the use of pseudofermions.