Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

Abstract

We study quantum magnetism of interacting spinor bosons at integer fillings hopping in a square lattice in the presence of non-Abelian gauge fields. In the strong coupling limit, it leads to the Rotated ferromagnetic Heisenberg model (RFHM) which is a new class of quantum spin model. We introduce Wilson loops to characterize frustrations and gauge equivalent classes. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground state. It supports not only commensurate magnons, but also a new gapped elementary excitation: in-commensurate magnons with two gap minima continuously tuned by the SOC strength. At low temperatures, these magnons lead to dramatic effects in many physical quantities such as density of states, specific heat, magnetization, uniform susceptibility, staggered susceptibility and various spin correlation functions. The commensurate magnons lead to a pinned central peak in the angle resolved light or atom Bragg spectroscopy. However, the in-commensurate magnons split it into two located at their two gap minima. At high temperatures, the transverse spin structure factors depend on the SOC strength explicitly. The whole set of Wilson loops can be mapped out by measuring the specific heat at the corresponding orders in the high temperature expansion. We argue that one gauge may be realized in current experiments and other gauges may also be realized in near future experiments. The results achieved along the exact solvable line sets up the stage to investigate dramatic effects when tuning away from it by various means. We sketch the crucial roles to be played by these magnons at other equivalent classes, with spin anisotropic interactions and in the presence of finite magnetic fields. Various experimental detections of these new phenomena are discussed. Rotated Anti-ferromagnetic Heisenberg model are also briefly mentioned.

18 pages main text, 10 figures; accepted for publication in Phy. Rev. A

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Cited by in corpus (12)

• High Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases
• Hubbard model with Rashba or Dresselhaus spin-orbit coupling and Rotated Anti-ferromagnetic Heisenberg Model
• Classification of magnons in Rotated Ferromagnetic Heisenberg model and their competing responses in transverse fields
• Topological depletions and sub-leading scalings across topological phase transitions
• Exotic Spin Phases in Two Dimensional Spin-orbit Coupled Models: Importance of Quantum Fluctuation Effects
• Parity oscillations and photon correlation functions in the $Z_2/U(1)$ Dicke model at a finite number of atoms or qubits
• High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice
• Synthetic spin-orbit coupling for the multispin models in optical lattices
• Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors
• Topological Charge Quadrupole Protected by Spin-Orbit U(1) Quasi-Symmetry in Antiferromagnet NdBiPt
• Slow-Goldstone mode generated by order from quantum disorder and its experimental detection
• Bose-Einstein condensations of magnons in quantum magnets with spin-orbit coupling in a Zeeman field