Cumulant $t$-expansion for strongly correlated fermions

TL;DR

This paper introduces a nonperturbative cumulant t-expansion scheme to accurately compute ground state energies of strongly correlated fermion models, demonstrating its effectiveness on spinless fermions in multiple dimensions.

Contribution

The paper develops an automated cumulant calculation method combined with a novel extrapolation technique for the t-expansion to determine ground state energies.

Findings

Exact calculation of cumulants up to 8th order for spinless fermions.

Converging energy approximations for 1D, 2D, and 3D models.

Effective nonperturbative approach for strongly correlated fermion systems.

Abstract

A systematic nonperturbative scheme is implemented to calculate the ground state energy for a wide class of strongly correlated fermion models. The scheme includes: (a) method of automatic calculations of the cumulants of the model Hamiltonian; (b) method of the ground state energy calculation from these cumulants using the $t$-expansion proposed by Horn and Weinstein [Phys. Rev. D \textbf{30}, 1256 (1984)] with new procedure of its extrapolation to $t\rightarrow\infty$. As an example of application of the method all cumulants up to the 8-th order for spinless fermion model are calculated exactly, and converging sequences of approximations to the ground state energy are obtained for one-, two- and three-dimensional versions of the model.