Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases

Abstract

We study the odd integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a novel universality class, with critical exponents associated with the divergence of the correlation length $\nu \approx 2/3$ and the order parameter susceptibility $\gamma \approx 1/2$. We solve the effective spin model exactly using the density matrix renormalization group, and compare with both a large-$S$ classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.

arXiv comment15 pages, 14 figures, replaced with published version

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• A comprehensive review on developments of synthetic dimensions
• $\mathbb{C}{P}^2$ Skyrmion Crystals in an SU(3) Magnet with a Generalized Dzyaloshinskii-Moriya Interaction
• Tunable-spin-model generation with spin-orbit-coupled fermions in optical lattices
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• Dynamics of spin-orbit-coupled cold atomic gases in a Floquet lattice with an impurity
• Strongly interacting spin-orbit coupled Bose-Einstein condensates in one dimension
• Quantum spiral spin-tensor magnetism
• Synthetic Hall tube of interacting fermions
• Spin-orbit coupled bosons in one dimension: emergent gauge field and Lifshitz transition