<i>Ab initio</i> finite-temperature and excited state computations by auxiliary-field quantum Monte Carlo

Development in the ground-state auxiliary-field quantum Monte Carlo (AFQMC) approach over the past decade has allowed accurate computations in a broad array of systems ranging from Hubbard-like models, ultracold Fermi gases, to solids and quantum chemistry. I will discuss recent progress in generailizing the approach to non-zero temperatures. Two bottlenecks had to be removed. The first is the sign or phase problem which appears in most cases, similar to ground-state calculations. The second is the unfavorable scaling of finite-temperature, grand-canonical computations as N^3 (N is the size of the lattice or basis set) in contrast with N*M^2 in ground-state computations (M is the number of fermions), a major obstacle in any realistic calculations aiming to describe the continuum limit, where N/M needs to be extrapolated to infinity for convergence. We remove the sign or phase problem by constraining the path-integrals in field space with a gauge condition; a self-consistent procedure is formulated to improve the accuracy of the constraint iteratively [1]. We then introduce a systematically controllable low rank factorization which changes the scaling of the computations to N*M^2 [2]. The method is applicable to both models and real materials. Results will be presented on magnetic and stripe orders in the repulsive Hubbard model, as well as pairing and other properties in the strongly interacting two-dimensional Fermi gas as a function of temperature.

[1] Yuan-Yao He et al, Phys. Rev. B 99, 045108 (2019).
[2] Yuan-Yao He, Hao Shi, Shiwei Zhang, Phys. Rev. Lett. 123, 136402 (2019).