The Hubbard dimer within the Green's function equation of motion approach

TL;DR

This paper presents a Green's function equation of motion approach for the Hubbard dimer, addressing numerical challenges at low temperatures by leveraging total spin quantum numbers.

Contribution

It introduces a formulation that computes unknown averages via a linear system and solves the numerical instability issue using total spin symmetry.

Findings

Linear system approach is feasible at all finite temperatures.

Using total spin reduces the condition number problem.

Method improves numerical stability for the Hubbard dimer.

Abstract

We consider a formulation of the equation of motion technique for Green's function in which the unknown averages are computed by solving a linear system. This linear system appears solvable for all finite temperatures, but depending on the system parameters the condition number can be very large, making the solution numerically unfeasible at low temperatures. In the example that we consider, the Hubbard dimer, we can get rid of this problem by making use of total spin as a good quantum number.