Lefschetz thimble Monte Carlo for many-body theories: A Hubbard model study

Recently, a method based on stochastic integration on the surfaces of steepest descent of the action was introduced to tackle the sign problem in quantum-field theories. We show how this method can be used in many-body theories to perform fully nonperturbative calculations of quantum corrections about mean-field solutions. We discuss an explicit algorithm for implementing our method, and present results for the repulsive Hubbard model away from half-filling at intermediate temperatures. Our results are consistent with those from other state-of-the-art calculations.

Figure 1

Double occupancy vs number density for the repulsive Hubbard model. Our results are shown with filled red squares, while the results from extrapolated DCA [18] are shown with filled blue circles. The error bars, where not visible, are smaller than the size of the symbols. The lines are meant as a guide to the eye.

Figure 2

Our results (solid red squares) for double occupancy, effective hopping parameter, and energy vs temperature at $\mu /t=-1.0$ for the repulsive Hubbard model. The blue solid lines in the top panel are results from resummed NLCE calculations [19]. The error bars, where not visible, are smaller than the size of the symbols. The dotted lines are meant as a guide to the eye.