Exotic Quantum Spin Models in Spin-Orbit-Coupled Mott Insulators

Abstract

We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and "localized Wannier states method" and derive the low-energy spin Hamiltonian for bosons and fermions. The spin Hamiltonian is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interactions and it has a rich classical phase diagram with collinear, spiral and vortex phases. We discuss the state of the art of experiments to realize and detect magnetic orderings in strongly correlated optical lattices.

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

“…(2) becomes classical. Some interesting results on the possible rich classical ground states at some sets of general (α, β) in the Heisenberg-Kitaev-DM representation were attempted numerically in [25,26]. Here, we plan to study the quantum phenomena in the RH model at generic (α, β).…”

Bose-Bose mixtures with synthetic spin-orbit coupling in optical lattices

“…In particular, in the strongly interacting regime, a super-exchange spin model with Dzyaloshinskii-Moriya (DM) type interactions [17,18] can be derived by second-order perturbation theory. And various exotic spin-textures are predicted by classical Monte-Carlo simulations or spin-wave analysis of the effective spin model [12][13][14][15]. Similar spin textures induced by the DM-type interactions have also been found in various solid state materials and attracted great interest [19][20][21].…”

“…This has motivated experimental developments in the field of quantum simulation with ultracold atoms, where tunable SO coupling and more generally synthetic non-abelian gauge fields are created in both neutral bosonic atoms [5][6][7] and fermionic atoms [8,9] via Raman processes or by driven optical lattices [10]. This progress has stimulated interesting studies on the physics of SO coupled Bose-Bose mixtures subjected to an optical lattice [11][12][13][14][15][16], where the Mott insulator to superfluid phase transition [11,12], magnetic order in the deep Mott insulator regime [12][13][14][15], and superfluid phases [11,12,14,16] are investigated. In particular, in the strongly interacting regime, a super-exchange spin model with Dzyaloshinskii-Moriya (DM) type interactions [17,18] can be derived by second-order perturbation theory.…”

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

“…The realisation of the deep XY-regime with this particular driving protocol is limited, since |J 2 (4ζ Φ )| < 1 but, at finite S z S z -interaction a semi-classical study showed that vortices persist and can be thought of as half-skyrmion configurations of the Neél field [48][49][50]. Another interesting feature of the spin Hamiltonian is that it exhibits a Dzyaloshinskii-Moriya (DM) interaction term [51][52][53][54], D mn · (S m+1,n × S mn ). The DM coupling is spatially-dependent, polarised along the z-direction D mn = sin(φ mn )J 2 (4ζ Φ )n z /2, and present only along the x-lattice direction.…”