Magnon Condensation in Dimerized Antiferromagnets with Spin-Orbit Coupling

Bose-Einstein condensation (BEC) of triplet excitations triggered by a magnetic field, sometimes called magnon BEC, in dimerized antiferromagnets gives rise to a long-range antiferromagnetic order in the plane perpendicular to the applied magnetic field. To explore the effects of spin-orbit coupling on magnon condensation, we study the spin model on the distorted honeycomb lattice with dimerized Heisenberg exchange ($J$ terms) and uniform off-diagonal exchange ($Gamma$ terms) interactions. By using variational Monte Carlo method and spin wave theory, we find that an out-of-plane magnetic field can induce different types of long-range magnetic orders, no matter if the ground state is a non-magnetic dimerized state or an antiferromagnetically ordered N{e}el state. Furthermore, the critical properties of field-driven phase transitions in systems with spin-orbit coupling can be different from the conventional magnon BEC. Our study is helpful to understand the rich phases of spin-orbit coupled antiferromagnets in an external magnetic field.

Symmetry Invariants of Spin Space Groups in Magnetic Materials

The spin rotations and lattice rotations are locked in the Shubnikov magnetic space groups in describing magnetically ordered materials. However, real materials may contain symmetry elements whose spin and lattice operations are partially unlocked. These groups are called spin space groups and may give rise to new band structures for itinerant electrons. In the present work, we focus on potential magnetic materials in which the intrinsic electronic spin-orbit coupling is negligible. We theoretically predict many new fermionic quasiparticles at the high symmetry points (HSPs) or high symmetry lines (HSLs) in the Brillouin zone (BZ), which can neither be realized in non-magnetic systems nor in magnetic ones with Shubnikov magnetic space group symmetries. These new quasiparticles are characterized by the symmetry invariants of the little co-group, which are more essential than the representations (Reps) themselves. We also provide the dispersion around the high-symmetry points/lines, and predict a large class of nodal-point or nodal-line semimetals.

Non-Abelian Chiral Spin Liquid on the Kagome Lattice

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.

Chiral Topological Orders in an Optical Raman Lattice

We find an optical Raman lattice without spin-orbit coupling showing chiral topological orders for cold atoms. Two incident plane-wave lasers are applied to generate simultaneously a double-well square lattice and periodic Raman couplings, the latter of which drive the nearest-neighbor hopping and create a staggered flux pattern across the lattice. Such a minimal setup is can yield the quantum anomalous Hall effect in the single particle regime, while in the interacting regime it achieves the $J_1$-$J_2$-$K$ model with all parameters controllable, which supports a chiral spin liquid phase. We further show that heating in the present optical Raman lattice is reduced by more than one order of magnitude compared with the conventional laser-assisted tunneling schemes. This suggests that the predicted topological states be well reachable with the current experimental capability.