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



Ian B. Spielman, William Cole, Jed Pixley, Sankar Das Sarma, Matteo Rizzi


We study the Mott insulating phases at odd-integer filling in the spin-1 Bose-Hubbard chain and their fate in the presence of Raman spin-orbit coupling which has been achieved in ultracold atomic systems. We first derive the effective spin model in the strong coupling limit, which is a spin-1 ferromagnetic bilinear-biquadratic chain in a spiral magnetic field. We solve this effective spin model using the density matrix renormalization group and determine the resulting phase diagram as a function of the magnetic field strength and the biquadratic interaction. The ferromagnetic and dimerized phases that exist in the absence of spin-orbit coupling survive, but inherit spin- spiral structure. At large magnetic field strengths both of these phases are suppressed and become spiral paramagnets. We show that the ferromagnetic spiral phase can be qualitatively captured by a large-S classical solution and a phenomenological Landau theory. We determine the critical properties of the field tuned spiral ferromagnet-to-paramagnet phase transition and compute the critical exponents associated with the divergence of the correlation length ν ≈ 2/3 and the order parameter susceptibility γ ≈ 1/2. Our estimate of ν on a d = 1 quantum spin chain at T = 0 is consistent with the classical universality class of unaxial dipolar ferromagnets and the two component chiral spin liquid in d = 1 + 1. We discuss how these magnetic phases can be probed in ultracold atomic experiments on spin-1 bosons in an optical lattice.
Physical Review X


Mott Insulator, lattice


Spielman, I. , Cole, W. , Pixley, J. , Das, S. and Rizzi, M. (2017), Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases, Physical Review X, [online], (Accessed May 22, 2024)


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Created August 23, 2017, Updated April 2, 2018