The XYZ chain with Dzyaloshinsky-Moriya interactions: From spin-orbit-coupled lattice bosons to interacting Kitaev chains

Sebastiano Peotta*, Leonardo Mazza, Ettore Vicari, Marco Polini, Rosario Fazio, Davide Rossini

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

24 Citations (Scopus)

Abstract

Using the density-matrix renormalization group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger liquid behavior. Transitions from ferromagnetic to Luttinger liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term splits this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.

Original languageEnglish
Article numberP09005
Pages (from-to)1-17
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2014
Issue number9
DOIs
Publication statusPublished - 1 Sep 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • ladders and planes (theory)
  • optical lattices
  • quantum phase transitions (theory)
  • quantum wires (theory)
  • spin chains

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