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arXiv:1705.06742 · Physical Review A

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

J. H. Pixley, William S. Cole, Ian B. Spielman, Matteo Rizzi, S. Das Sarma

Published Oct 23, 2017• 12 citations
arXivHTMLPDF

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 universality class with critical exponents associated with the divergence of the correlation length $\ensuremath{\nu}\ensuremath{\approx}2/3$ and the order-parameter susceptibility $\ensuremath{\gamma}\ensuremath{\approx}1/2$. 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.

DOI
10.1103/physreva.96.043622

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Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S = 1 Heisenberg model with biquadratic interaction.
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