Four electrons in a two-leg Hubbard ladder: exact ground states

TL;DR

This paper presents an exact method to determine the ground state of four electrons in a two-leg Hubbard ladder, providing insights into few-particle quantum states with potential technological applications.

Contribution

The authors develop a tractable, exact procedure for solving the four-particle ground state in large lattice systems using symmetry-adapted basis functions.

Findings

Exact ground state equations derived for four electrons

Method applicable to other few-particle systems

Provides detailed quantum state characterization

Abstract

In the case of a two-leg Hubbard ladder we present a procedure which allows the exact deduction of the ground state for the four particle problem in arbitrary large lattice system, in a tractable manner, which involves only a reduced Hilbert space region containing the ground state. In the presented case, the method leads to nine analytic, linear, and coupled equations providing the ground state. The procedure which is applicable to few particle problems and other systems as well is based on an r-space representation of the wave functions and construction of symmetry adapted orthogonal basis wave vectors describing the Hilbert space region containing the ground state. Once the ground state is deduced, a complete quantum mechanical characterization of the studied state can be given. Since the analytic structure of the ground state becomes visible during the use of the method, its importance is not reduced only to the understanding of theoretical aspects connected to exact descriptions or potential numerical approximation scheme developments, but is relevant as well for a large number of potential technological application possibilities placed between nano-devices and quantum calculations, where the few particle behavior and deep understanding are important key aspects to know.