Construction of size-consistent effective Hamiltonians for systems with arbitrary Hilbert space

TL;DR

This paper introduces a cumulant-based method for constructing size-consistent effective Hamiltonians applicable to systems with arbitrary Hilbert spaces, demonstrated on the Hubbard model in the strong-coupling limit.

Contribution

The paper presents a novel cumulant-based approach for effective Hamiltonian construction that guarantees size consistency across arbitrary Hilbert spaces.

Findings

Derived the fourth-order expansion of the effective Hamiltonian for the Hubbard model

Demonstrated size consistency in the constructed Hamiltonians

Applied the method to systems in arbitrary spatial dimensions

Abstract

Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other treatments. As a nontrivial example of use the derived method is applied to the strong-coupling limit of the half-filled Hubbard model on a general lattice in arbitrary spatial dimension for which the fourth-order expansion in t/U of the effective Hamiltonian is derived.