Exact ground states for the four-electron problem in a Hubbard ladder

TL;DR

This paper derives the exact ground state energy and wave function for four electrons in a large two-leg Hubbard ladder using an explicit basis construction and solving a system of nine linear equations.

Contribution

It introduces a method to analytically determine the ground state of four electrons in a Hubbard ladder through basis construction and linear equation systems.

Findings

Exact ground state energy and wave function obtained

Method applicable to large Hubbard ladders

Provides explicit analytical solutions

Abstract

The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The method is based on the construction in r-space of the different type of orthogonal basis wave vectors which span the subspace of the Hilbert space containing the ground state. In order to do this, we start from the possible microconfigurations of the four particles within the system. These microconfigurations are then rotated, translated and spin-reversed in order to build up the basis vectors of the problem. A closed system of nine analytic linear equations is obtained whose secular equation, by its minimum energy solution, provides the ground state energy and the ground state wave function of the model.