Spin-Orbit Coupled Bosons in One Dimension: Entanglement Entropy and Dynamics

We study the entanglement and dynamical properties of a spin-orbit coupled Bosons which describe one-dimension ultracold atoms with Raman-induced spin-orbit coupling. The two component spin-orbit coupled Bose liquid was proposed as a platform for studying quantum criticality in itinerant magnets [1]. In the presence of strong spin-independent interactions and spin-orbit coupling, this spinor Bose liquid undergoes an interaction (or density) tuned quantum phase transition similar to those in itinerant magnetic solid state systems. Although the order parameter describes a broken Z₂ spin symmetry, the associated phase is qualitatively distinct from the Ising phase transition and has a dynamical critical exponent z≈2, typical of a Lifshitz transition. We discuss the unusual entanglement and dynamical features of this Lifshitz critical point stemming from its non-integrablility and absence of Lorentz symmetry.

[1] W. S. Cole, J. Lee, K. W. Mahmud, Y. Alavirad, I. Spielman, and J. D. Sau, arXiv:1711.05794.