title: 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.
authors.affiliation: Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland and Laboratoire de Physique, École Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France.
authors.forename: Laurent
authors.initials: L
authors.lastname: de Forges de Parny
authors.affiliation: Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
authors.forename: Hongyu
authors.initials: H
authors.lastname: Yang
authors.affiliation: Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
authors.forename: Frédéric
authors.initials: F
authors.lastname: Mila