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

Published

August 23, 2017

Author(s)

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

Abstract

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.

Citation

Physical Review X

Pub Type

Journals

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Keywords

Mott Insulator, lattice

Citation

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], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=923464 (Accessed April 19, 2024)