Finite Chains with Quantum Affine Symmetries

TL;DR

This paper extends the Hubbard model to include new interactions, derives an effective Hamiltonian in the strong coupling limit, and reveals its spectrum matches that of an anisotropic Heisenberg chain with explicit wave functions and symmetry analysis.

Contribution

It introduces a novel extension of the Hubbard model, derives the effective Hamiltonian in the strong U regime, and connects its spectrum to the XXZ model with explicit wave functions.

Findings

Spectrum of the effective Hamiltonian matches the XXZ model with Z field.

Wave functions are explicitly constructed from the XXZ model.

Degeneracies are explained via U_q(sl(2)} representations.

Abstract

We consider an extension of the (t-U) Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a one-dimensional open chain with L sites (4^L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3^L states. We show that the spectrum of the latter Hamiltonian (not the degeneracies) coincides with the spectrum of the anisotropic Heisenberg chain (XXZ model) in the presence of a Z field (2^L states). The wave functions of the 3^L-state system are obtained explicitly from those of the 2^L-state system, and the degeneracies can be understood in terms of irreducible representations of U_q(\hat{sl(2)}).