Imaginary time quantum Monte Carlo simulations of many fermion systems

I. Morgenstern

Wolfgang von der Linden, R. Preuss, Werner R. Hanke

Bayesian probability theory along with the maximum entropy concept is widely used for inferential problems, particularly to infer dynamic properties of strongly correlated fermion systems from quantum Monte Carlo (QMC) imaginary time data. In current QMC applications, however, the error covariance of the QMC data is not treated consistently. Here we present a consistent Bayesian analysis of all the information provided by the QMC simulation. This approach allows us to infer reliable results with the least amount of computer time.

Mauro Iazzi, Alexey A. Soluyanov, Matthias Troyer

Monte Carlo simulations are a powerful tool for elucidating the properties of complex systems, but when applied to fermionic quantum systems, quantum Monte Carlo (QMC) algorithms suffer from the so-called ``negative sign problem,'' causing the computational effort to grow exponentially with problem size. Here we demonstrate that the fermion sign problem originates in topological properties of the configurations. Using the widely used determinantal approaches, that remove the trivial sign problem due to particle exchange, we prove that the negative sign of a configuration is a topological invariant---an imaginary time counterpart of the Aharonov-Anandan phase---and reduces to a Berry phase in the adiabatic limit. This provides an intriguing connection between QMC simulations and classification of topological states.

Lucas Madeira

Yasuhiro Hatsugai, Masatoshi Imada

H.-B. Schüttler, Douglas J. Scalapino

We present a method to obtain dynamical correlation functions of quantum many-body systems in the real-frequency domain from Monte Carlo data of the corresponding imaginary-time Green's functions. The method is based on a least-squares-fit procedure to solve the integral equation relating imaginary-time and real-frequency correlation functions. To demonstrate its feasibility, we have applied our method to imaginary-time Monte Carlo data for the density correlation function of a simple model of interacting spinless fermions in one dimension. We compare our results to the analytical results, available in the limits of zero and strong interaction. We find that despite the presence of noise in the input data, the real-frequency spectra obtained with our method are qualitatively correct. They reflect accurately the particle-hole and the soliton-antisoliton excitations, present in the noninteracting and in the strongly coupled fermion system, respectively. We also compare our method to other approaches that have been proposed for obtaining dynamical correlation functions via Monte Carlo simulation.