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

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 turns out to split 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.

18 pages, 8 figures

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• Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction
• Analytical results for the unusual Grüneisen ratio in the quantum Ising model with Dzyaloshinskii-Moriya interaction
• Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases
• Magnetic phase transitions of insulating spin-orbit coupled Bose atoms in one-dimensional optical lattices
• Phases of d-orbital bosons in optical lattices
• Thermodynamics of a spin-1/2 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Spin-orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice
• Spin-orbit coupled bosons in one dimension: emergent gauge field and Lifshitz transition