Emergent gauge field and the Lifshitz transition of spin-orbit coupled bosons in one dimension

William S Cole,I B Spielman,Junhyun Lee,Jay D Sau,Khan W Mahmud,Yahya Alavirad

doi:10.1038/s41598-019-43929-6

Abstract

In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction- or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken Z2 inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent z ≃ 2, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.

Highlights

Perhaps the first example of a quantum phase transition (QPT) was Stoner’s identification of a zero-temperature critical point distinguishing between unpolarized and spin-imbalanced Fermi liquids, and magnetic transitions in Fermi liquids have remained a rich subject since
In the Bose liquid, fluctuations of the spin degree of freedom behave as an emergent dynamical gauge field for the SF sound mode, the former coupled to the latter by an emergent electric field, as we show in this work
In the presence of a helical Zeeman field we find that there is a curve of quantum critical points of the system that can be reached by tuning interaction or density; in other words, sufficiently strong interactions can disorder the

Summary

Introduction

Perhaps the first example of a quantum phase transition (QPT) was Stoner’s identification of a zero-temperature critical point distinguishing between unpolarized and spin-imbalanced Fermi liquids, and magnetic transitions in Fermi liquids have remained a rich subject since These transitions for gapless, itinerant magnets belong to a class that is qualitatively distinct from transitions between gapped phases of matter and still remain mysterious despite the seminal works by Hertz and Millis[1,2,3]. In the strongly interacting limit of interest to us it is more natural to understand the transition in terms of the competition between Zeeman energy and spin stiffness, the generalized rigidity associated with the interacting ferromagnetic Bose liquid.

Objectives

Methods

Results

Conclusion