Finite-temperature auxiliary-field Quantum Monte Carlo study of dynamical correlation functions in correlated fermion systems

We compute dynamical (imaginary-time) correlation functions in correlated fermion systems using the finite-temperature auxiliary-field Quantum Monte Carlo method. The sign problem is eliminated by introducing constraints in auxiliary-field space. We carry out a systematic benchmark study of dynamical correlation functions in the two-dimensional repulsive Hubbard model, for various interaction strengths, density, and temperatures. At high temperatures, essentially exact results are obtained independent of the form of the constraint, similar to calculations of static quantities [1]. With decreasing temperature, we discuss how the constraint can be optimized to improve the accuracy of dynamical correlation functions. In the context of studying the pseudogap behavior, we apply the method to compute the self-energy and spectral functions in the Hubbard model.
References:
[1] Yuan-Yao He, Mingpu Qin, Hao Shi, Zhong-Yi Lu, Shiwei Zhang, Phys. Rev. B 99, 045108 (2016).