Fermionic representations of integrable lattice systems

TL;DR

This paper introduces a general fermionic framework for integrable lattice systems, allowing Hamiltonian and symmetry representations via Fermi operators, exemplified by the Hubbard model at infinite coupling.

Contribution

It presents a novel scheme to derive fermionic Hamiltonians and symmetry generators from solutions of the Yang-Baxter equation in integrable systems.

Findings

Fermionic Hamiltonians can be directly obtained from Yang-Baxter solutions.

The approach is demonstrated on the Hubbard model at infinite coupling.

Fermionic representations simplify the analysis of integrable lattice models.

Abstract

We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the Yang-Baxter equation and to express the corresponding $L$-matrix and the generators of symmetries in terms of Fermi operators. We illustrate our approach through a number of examples. Our main example is the algebraic Bethe ansatz solution of the Hubbard model in the infinite coupling limit.