FInite-temperature Auxiliary-Field Quantum Monte Carlo: Recent Developments and Applications*

We present a highly accurate auxiliary-field quantum Monte Carlo (AFQMC) method to study finite-temperature properties of correlated fermion systems. This approach eliminates the minus sign problem by introducing constraints in auxiliary-field space. Building on earlier ideas [1] and incorporating the latest developments in zero-temperature methods, we introduce a self-consistent formalism [2] to improve the constraint in the finite-temperature framework. This with several other algorithmic advances leads to a more accurate, more efficient, and numerically more stable approach for finite-temperature calculations. We carry out systematic benchmark study in the 2D Hubbard model. Temperatures as low as T=1/80 (in units of hopping) are reached. The finite-temperature method is exact at high temperatures, and approaches the result of the zero-temperature constrained-path AFQMC as temperature is lowered. The benchmark shows that systematically accurate results are obtained for thermodynamic properties. The properties of the 2D doped Hubbard model as functions of temperature will be presented and discussed.

[1] Shiwei Zhang, Phys. Rev. Lett. 83, 2777 (1999).
[2] Mingpu Qin, Hao Shi, and Shiwei Zhang, Phys. Rev. B 94, 235119 (2016).