Scalar Symmetries of the Hubbard Models with Variable Range Hopping

TL;DR

This paper identifies scalar conserved currents in various Hubbard models with variable range hopping, providing evidence for the integrability of the elliptic version and explicitly constructing two-electron wave functions.

Contribution

It introduces scalar conserved currents for different Hubbard models and supports the integrability hypothesis for the elliptic case with explicit wave functions.

Findings

Scalar conserved currents are found for trigonometric, hyperbolic, and elliptic Hubbard models.

Supports the hypothesis that the elliptic Hubbard model is integrable.

Explicit two-electron wave functions are constructed for these models.

Abstract

Examples of scalar conserved currents are presented for trigonometric, hyperbolic and elliptic versions of the Hubbard model with non-nearest neighbour variable range hopping. They support for the first time the hypothesis about the integrability of the elliptic version. The two- electron wave functions are constructed in an explicit form.