Incremental expansions for the ground state energy of the two-dimensional Hubbard model

TL;DR

This paper extends the method of increments to two-dimensional Hubbard models, demonstrating that accurate ground state energies can be obtained efficiently using small lattice segments, with results comparable to other advanced methods.

Contribution

The paper generalizes the incremental expansion approach to 2D Hubbard models and explicitly treats up to third order, improving computational efficiency and accuracy.

Findings

Incremental expansions are highly efficient for 2D Hubbard models.

Good accuracy achieved with small lattice segments of 8 sites.

Results compare favorably with Monte Carlo and cumulant methods.

Abstract

A generalization of Faddeev's approach of the 3-body problem to the many-body problem leads to the method of increments. This method was recently applied to account for the ground state properties of Hubbard-Peierls chains (JETP Letters 67 (1998) 1052). Here we generalize this approach to two-dimensional square lattices and explicitely treat the incremental expansion up to third order. Comparing our numerical results with various other approaches (Monte Carlo, cumulant approaches) we show that incremental expansions are very efficient because good accuracy with those approaches is achieved treating lattice segments composed of 8 sites only.