Anderson tower of states and nematic order of spin-1 bosonic atoms on a 2D lattice

Abstract

We investigate the structure of the spectrum of antiferromagnetically coupled spin-1 bosons on a square lattice using degenerate perturbation theory and exact diagonalizations of finite clusters. We show that the superfluid phase develops an Anderson tower of states typical of nematic long-range order with broken SU(2) symmetry.We further show that this order persists into the Mott insulating phase down to zero hopping for one boson per site, and down to a critical hopping for two bosons per site, in agreement with mean-field and Quantum Monte Carlo results. The connection with the transition between a fragmented condensate and a polar one in a single trap is briefly discussed.

5 pages, 4 figures + 5 pages of supplemental material

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Cited by in corpus (11)

• Spin nematic order in antiferromagnetic spinor condensates
• Semi-classical simulation of spin-1 magnets
• Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice
• Reconstruction of classical skyrmions from Anderson towers: quantum Darwinism in action
• Mott lobes of the $S=1$ Bose-Hubbard model with three-body interactions
• Gravitational wave analogues in spin nematics and cold atoms
• Spin nematics next to spin singlets
• Abundant quadrupolar or nematic phases driven by the Heisenberg interactions in a spin-1 dimer system forming a bilayer
• Phase Diagrams of Antiferromagnetic Spin-1 Bosons on Square Optical Lattice with the Quadratic Zeeman Effect
• Dynamical instability in the S=1 Bose-Hubbard model
• Magnetic Phase Transition in the Ground-State Phase Diagram of Binary Bose Gases in Optical Lattices