Flat histogram diagrammatic Monte Carlo method: calculation of the Green's function in imaginary time

Reducing autocorrelation time in determinant quantum Monte Carlo using the Wang-Landau algorithm: Application to the Holstein model

When performing a Monte Carlo calculation, the running time should, in principle, be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its particularly long autocorrelation time. In this paper, we employ the Wang-Landau algorithm in the determinant quantum Monte Carlo to achieve the flat-histogram sampling in the "configuration weight space," which can greatly reduce the autocorrelation time by sacrificing some sampling efficiency. The proposal is checked in the Holstein model on both square and honeycomb lattices. Based on such a Wang-Landau assisted determinant quantum Monte Carlo method, some models with long autocorrelation times can now be simulated possibly.

Monte Carlo algorithm for free energy calculation

We propose a Monte Carlo algorithm for the free energy calculation based on configuration space sampling. An upward or downward temperature scan can be used to produce F(T). We implement this algorithm for the Ising model on a square lattice and triangular lattice. Comparison with the exact free energy shows an excellent agreement. We analyze the properties of this algorithm and compare it with the Wang-Landau algorithm, which samples in energy space. This method is applicable to general classical statistical models. The possibility of extending it to quantum systems is discussed.