Numerical Study of the One-Dimensional Spin-Orbit Coupled System with SU(2)<b> ⊗</b>SU(2) Symmetry

Abstract

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