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Publication# 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.

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Ontological neighbourhood

Boson

In particle physics, a boson (ˈboʊzɒn ˈboʊsɒn) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spin (, , , ...). Every observed subatomic particle is either a boson or a fermion. Some bosons are elementary particles occupying a special role in particle physics, distinct from the role of fermions (which are sometimes described as the constituents of "ordinary matter").

W and Z bosons

In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are _W boson+, _W boson-, and _Z boson0. The _W boson+- bosons have either a positive or negative electric charge of 1 elementary charge and are each other's antiparticles. The _Z boson0 boson is electrically neutral and is its own antiparticle. The three particles each have a spin of 1.

Gauge boson

In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons, usually as virtual particles. Photons, W and Z bosons, and gluons are gauge bosons. All known gauge bosons have a spin of 1; for comparison, the Higgs boson has spin zero and the hypothetical graviton has a spin of 2. Therefore, all known gauge bosons are vector bosons.

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