Lie Algebraic Similarity Transformed Hamiltonians for Lattice Model Systems

TL;DR

This paper introduces a Lie algebraic similarity transformation approach for lattice models, enabling efficient and accurate solutions of the Hubbard model across various interaction strengths.

Contribution

The paper develops an exact summation of Hausdorff series for Lie algebraic transformations applied to lattice Hamiltonians, facilitating polynomial-cost solutions.

Findings

Accurate results for 1D and 2D Hubbard models across all interaction strengths.

Transformation generates locally weighted orbital transformations.

Biorthogonal mean-field approach effectively solves the non-hermitian Hamiltonian.

Abstract

We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor $n_{i\uparrow}n_{i\downarrow}$, and two-site products of density $(n_{i\uparrow} + n_{i\downarrow})$ and spin $(n_{i\uparrow}-n_{i\downarrow})$ operators. The resulting non-hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the 1D and 2D repulsive Hubbard model where we find accurate results across all interaction strengths.