Abstract
We generalize the $\eta$-pairing theory in Hubbard models to the ones with spin-orbit coupling (SOC) and obtain the conditions under which the $\eta$-pairing operator is an eigenoperator of the Hamiltonian. The $\eta$ pairing thus reveals an exact $SU(2)$ pseudospin symmetry in our spin-orbit coupled Hubbard model, even though the $SU(2)$ spin symmetry is explicitly broken by the SOC. In particular, these exact results can be applied to a variety of Hubbard models with SOC on either bipartite or non-bipartite lattices, whose noninteracting limit can be a Dirac semimetal, a Weyl semimetal, a nodal-line semimetal, and a Chern insulator. The $\eta$ pairing conditions also impose constraints on the band topology of these systems. We then construct and focus on an interacting Dirac-semimetal model, which exhibits an exact pseudospin symmetry with fine-tuned parameters. The stability regions for the exact $\eta$-pairing ground states (with momentum $\bm{\pi}$ or $\bm{0}$) and the exact charge-density-wave ground states are established. Between these distinct symmetry-breaking phases, there exists an exactly solvable multicritical line. In the end, we discuss possible experimental realizations of our results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.