Quantum field theory of nematic transitions in spin orbit coupled spin-1 polar bosons

Abstract

We theoretically study an ultra-cold gas of spin-1 polar bosons in a one dimensional continuum which are subject to linear and quadratic Zeeman fields and a Raman induced spin-orbit coupling. Concentrating on the regime in which the background fields can be treated perturbatively we analytically solve the model in its low-energy sector, i.e. we characterize the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field $\epsilon$, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-disordered superfluid phase at strong coupling. We employ a combination of renormalization group calculations and duality transformations to access the nature of the phase transitions. At $\epsilon =0$, a line of spin-charge separated pairs of Luttinger liquids divides the two nematic phases and the transition to the spin disordered state at strong coupling is of the Berezinskii-Kosterlitz-Thouless type. In contrast, at $\epsilon \ne 0$, the quantum critical theory separating nematic and strong coupling spin disordered phases contains a Luttinger liquid in the charge sector that is coupled to a Majorana fermion in the spin sector (i.e. the critical theory at finite $\epsilon$ maps to a quantum critical Ising model that is coupled to the charge Luttinger liquid). Due to an emergent Lorentz symmetry, both have the same, logarithmically diverging velocity. We discuss the experimental signatures of our findings that are relevant to ongoing experiments in ultra-cold atomic gases of ${}^{23}$Na.

arXiv comment5 pages main text, 4 figures. 8 pages of supplement

References in corpus (44)

• A spin-orbit coupled Bose-Einstein condensate
• Spinor Bose Condensates in Optical Traps
• Synthetic magnetic fields for ultracold neutral atoms
• Bose-Einstein condensation with internal degrees of freedom in alkali atom gases
• Spin-orbit coupling in quantum gases
• Spinor Bose-Einstein condensates
• Spin-Orbit Coupled Degenerate Fermi Gases
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Experimental realization of a two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases
• Quantum tri-criticality and phase transitions in spin-orbit coupled Bose-Einstein condensates
• Superstripes and the excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate
• Resonant control of spin dynamics in ultracold quantum gases by microwave dressing
• Itinerant magnetism in spin-orbit coupled Bose gases
• Emergent Rank-5 'Nematic' Order in URu2Si2
• Observation of symmetry-protected topological band with ultracold fermions
• Spin correlation and Discrete symmetry in Spinor Bose-Einstein Condensates
• Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate
• Topological defects and the superfluid transition of the $s=1$ spinor condensate in two dimensions
• The Raman dressed spin-1 spin-orbit coupled quantum gas
• Tricriticalities and Quantum Phases in Spin-Orbit-Coupled Spin-$1$ Bose Gases
• Phase diagram of spin 1 antiferromagnetic Bose-Einstein condensates
• Approach for making visible and stable stripes in a spin-orbit-coupled Bose-Einstein superfluid
• Symmetry classification of spin-orbit coupled spinor Bose-Einstein condensates
• Interacting spin-orbit-coupled spin-1 Bose-Einstein condensates
• Pairing in Luttinger Liquids and Quantum Hall States
• Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate
• Emergent Lorentz symmetry with vanishing velocity in a critical two-subband quantum wire
• Phase transitions and elementary excitations in spin-1 Bose gases with Raman-induced spin-orbit coupling
• Spin nematic order in antiferromagnetic spinor condensates
• Striped Ferronematic ground states in a spin-orbit coupled $S=1$ Bose gas
• Phase Transitions of S=1 Spinor Condensates in an Optical Lattice
• Thermal Phase Transitions of Strongly Correlated Bosons with Spin-Orbit Coupling
• The phase diagram of 2D polar condensates in a magnetic field
• Non-universal ordering of spin and charge in stripe phases
• Stepwise Bose-Einstein condensation in a spinor gas
• On the spin-liquid phase of one dimensional spin-1 bosons
• Real space mean-field theory of a spin-1 Bose gas in synthetic dimensions
• Fourier transform spectroscopy of a spin-orbit coupled Bose gas
• Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson
• Interaction driven exotic quantum phases in spin-orbit coupled spin$-1$ bosons
• Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases
• Spin-dependent Bragg spectroscopy of a spinor Bose gas
• Magnetically Stabilized Order. II: Critical states and algebraically ordered nematic spin liquids in one-dimensional optical lattices

Cited by in corpus (11)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• A comprehensive review on developments of synthetic dimensions
• Berezinskii-Kosterlitz-Thouless transition of spin-1 spinor Bose gases in the presence of the quadratic Zeeman effect
• Orientational order parameters for arbitrary quantum systems
• Many-body effects on second-order phase transitions in spinor Bose-Einstein condensates and breathing dynamics
• Topologically enabled superconductivity
• Strongly interacting spin-orbit coupled Bose-Einstein condensates in one dimension
• Quantum spiral spin-tensor magnetism
• Topological phases in pseudospin-1 Fermi gases with two-dimensional spin-orbit coupling
• Effective Spin-2 Quasi-particles at Linear Dispersive Five-fold Degenerate Points with Tunable Topological Chern Numbers
• Universal intrinsic higher-rank spin Hall effect