Universal Hubbard models with arbitrary symmetry

TL;DR

This paper introduces a universal framework for constructing integrable one-dimensional XX and Hubbard models with arbitrary symmetry, using a decomposition of vector spaces and the Quantum Inverse Scattering Method.

Contribution

It presents a general, symmetry-agnostic construction of integrable Hubbard models and their Bethe Ansatz solutions, extending previous models to arbitrary symmetries and infinite-dimensional spaces.

Findings

Explicit energy spectra and symmetry algebras derived.

Bethe Ansatz equations computed for certain sectors.

Perturbative analysis performed in the large coupling limit.

Abstract

We propose a general framework that leads to one-dimensional XX and Hubbard models in full generality, based on the decomposition of an arbitrary vector space (possibly infinite dimensional) into a direct sum of two subspaces, the two corresponding orthogonal projectors allowing one to define a R-matrix of a universal XX model, and then of a Hubbard model using a Shastry type construction. The QISM approach ensures integrability of the models, the properties of the obtained R-matrices leading to local Hubbard-like Hamiltonians. In all cases, the energies, the symmetry algebras and the scattering matrices are explicitly determined. The computation of the Bethe Ansatz equations for some subsectors of the universal Hubbard theories are determined, while they are fully computed in the XX case. A perturbative calculation in the large coupling regime is also done for the universal Hubbard models.