Numerical Study of the One-Dimensional Spin-Orbit Coupled System with SU(2)$\otimes$SU(2) Symmetry

TL;DR

This study numerically investigates a spin-orbit coupled model with SU(2)×SU(2) symmetry, revealing singular gap formation and discovering new critical phases near the SU(4) point, with detailed excitation behaviors.

Contribution

It provides the first numerical analysis of the SU(2)×SU(2) symmetric model, identifying novel critical phases and clarifying gap formation mechanisms.

Findings

Singular gap formation on the symmetric line.

Discovery of new critical phases around the SU(4) point.

Identification of massless continua in spin or orbital excitations.

Abstract

We numerically study the SU(2)$\otimes$SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially singular gap formation in consistent with the analytic approach, which is different from the previous numerical calculation. Furthermore, we find new critical phases around the SU(4) point, surrounding the previously known gapless symmetric line. In these novel phases either spin or orbital excitations around momentum $q=\pi$ form massless continua which split from the excitations belonging to the $[2^2]$ irreducible representation at the SU(4) point. On the critical symmetric line, the additional coupled spin-orbit excitations around $q=\pi/2$ originating from [$2^11^2$] become critical, too.