Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice

Abstract

We devise and benchmark a numerically exact quantum Monte Carlo (QMC) method for interacting electrons on a lattice, that we dub the alternating-basis QMC (ABQMC). The method is uniquely suited to evaluate charge and spin density and the corresponding correlation functions, in both direct and reciprocal space, imaginary or real time. The formalism applies in and out of thermal equillibrium, described by either the canonical or grand-canonical ensemble. The method relies on Suzuki-Trotter decomposition (STD) and owes flexibility to the representation of the kinetic and interaction terms in the many-body bases in which they are diagonal. We formulate a Monte Carlo (MC) update scheme that respects both the momentum and particle-number conservation laws, to restrict the configuration space and thus improve the efficiency of the sampling. To test the method, we perform various calculations for the Hubbard model on finite square lattices of up to 48 sites. We obtain the equation of state (density vs. chemical potential curve) in agreement with reference methods. We also evaluate the (real-time) dynamics of the survival probability of pure densitywave-like states: At small lattice sizes, where the exact diagonalization results are available, we demonstrate the validity of our method at short times; We then proceed to investigate this dynamics on the 4 × 4 Hubbard cluster. Finally, we discuss the extent of the fermionc sign problem and the current limitations of our method, both primarily related to the number of time-slices that we take in the STD.