The Hubbard model with spin orbit coupling: a lattice gauge theory approach

TL;DR

This paper investigates the Hubbard model with spin-orbit coupling using a lattice gauge theory approach, revealing conditions under which magnetic order and eta-pairing are suppressed due to gauge symmetry considerations.

Contribution

It introduces a lattice gauge theory framework to analyze the Hubbard model with spin-orbit interactions, providing rigorous results on the absence of certain orders under specific symmetry conditions.

Findings

Magnetic long-range order is ruled out when Rashba and Dresselhaus couplings are equal.

Eta-pairing is always ruled out regardless of parameters.

The gauge theory approach clarifies symmetry constraints in the model.

Abstract

We study the symmetry properties of the Hubbard model with spin-orbit interactions of Rashba and Dresselhaus type. These interactions break the rotational symmetry in spin space, so that the magnetic order cannot be excluded by using the Bogoliubov inequality method. Nevertheless, we rigorously show that the existence of the magnetic long-range orders may be ruled out when the Rashba and Dresselhaus coupling constants are equal in modulus, whereas the eta-pairing can be always ruled out, regardless of the microscopic parameters of the model. These results are obtained by imposing locally the SU(2) gauge symmetry on the lattice, and rewriting the spin-orbit interactions in such a way that they are included in the path ordered of the gauge field on lattice.