Rotated Heisenberg model and its applications to cold atom systems and Kitaev materials with SOC
This event is part of the Condensed Matter Theory Seminar Series.
Abstract: Recently, there are ground breaking experimental advances in generating 2 dimensional spin-orbit coupling (SOC) for cold atoms in both continuum and optical lattices. In materials, there are also 5d and 4d transition metal oxides with strong SOC which are so called Kitaev materials. We study interacting spionor bosons ( or fermions ) at integer ( or hall ) fillings on a square lattice in the presence of the SOC. In the strong coupling limit, it leads to Rotated Ferromagnetic ( Anti-ferromagnetic ) Heisenberg model ( RFHM or RAFHM ) which is a new class of quantum spin models with SOC. In this talk, we only focus on RFHM. For a solvable line in the SOC parameter space, we identify a new spin-orbital entangled commensurate ground state. It supports not only commensurate ( C ) magnons, but also a new gapped elementary excitation: in-commensurate ( IC) magnons with their two gap minima continuously tuned by the SOC parameter. A longitudinal Zeeman field will drag out these IC magnons and drive their condensations to various quantum Commensurate and In-commensurate phases. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at Mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Skyrmion (IC-SkX) crystal phases surrounded by the 4 commensurate phases. New excitation spectra above all the 5 phases are computed. Three different classes of quantum C-IC transitions from the IC-SKX to its 4 neighboring commensurate phases are identified. Then starting from the results achieved along the solvable line, we study the RFHM in the whole SOC parameter space. Its global phase diagram displays many quantum phenomena such as masses generated from "order from disorder " mechanism, quantum C and IC skyrmion phases, quantum Lifshitz C-IC transitions, spiral phases, metastable states, hysteresis, devil staircases and fractals, etc. Implications to cold atom systems and so called Kitaev materials with SOC are discussed. Various intriguing perspectives, especially on possible spin liquids in SOC lattice systems are outlined.