607 research outputs found
Vortex Molecules in Spinor Condensates
Condensates of atoms with spins can have vortices of several types; these are
related to the symmetry group of the atoms' ground state. We discuss how, when
a condensate is placed in a small magnetic field that breaks the spin symmetry,
these vortices may form bound states. Using symmetry classification of
vortex-charge and rough estimates for vortex interactions, one can show that
some configurations that are stable at zero temperature can decay at finite
temperatures by crossing over energy barriers. Our focus is cyclic spin 2
condensates, which have tetrahedral symmetry.Comment: 28 pages, 12 figure
Classifying Novel Phases of Spinor Atoms
We consider many-body states of bosonic spinor atoms which, at the mean-field
level, can be characterized by a single-particle wave function. Such states
include BEC phases and insulating Mott states with one atom per site. We
describe and apply a classification scheme that makes explicit spin symmetries
of such states and enables one to naturally analyze their collective modes and
topological excitations. Quite generally, the method allows classification of a
spin F system as a polyhedron with 2F vertices. After discussing the general
formalism we apply it to the many-body states of bosons with hyperfine spins
two and three. For spin-two atoms we find the ferromagnetic state, a continuum
of nematic states, and a state having the symmetry of the point group of the
regular tetrahedron. For spin-three atoms we obtain similar ferromagnetic and
nematic phases as well as states having symmetries of various types of
polyhedra with six vertices: the hexagon, the pyramid with pentagonal base, the
prism, and the octahedron.Comment: Added references, corrected typos, minor changes in tex
Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
The effect of interactions on topological insulators and superconductors
remains, to a large extent, an open problem. Here, we describe a framework for
classifying phases of one-dimensional interacting fermions, focusing on
spinless fermions with time-reversal symmetry and particle number parity
conservation, using concepts of entanglement. In agreement with an example
presented by Fidkowski \emph{et. al.} (Phys. Rev. B 81, 134509 (2010)), we find
that in the presence of interactions there are only eight distinct phases,
which obey a group structure. This is in contrast to the
classification in the non-interacting case. Each of these eight
phases is characterized by a unique set of bulk invariants, related to the
transformation laws of its entanglement (Schmidt) eigenstates under symmetry
operations, and has a characteristic degeneracy of its entanglement levels. If
translational symmetry is present, the number of distinct phases increases to
16.Comment: 12 pages, 1 figure; journal ref. adde
Topological phases in gapped edges of fractionalized systems
Recently, it has been proposed that exotic one-dimensional phases can be
realized by gapping out the edge states of a fractional topological insulator.
The low-energy edge degrees of freedom are described by a chain of coupled
parafermions. We introduce a classification scheme for the phases that can
occur in parafermionic chains. We find that the parafermions support both
topological symmetry fractionalized phases as well as phases in which the
parafermions condense. In the presence of additional symmetries, the phases
form a non-Abelian group. As a concrete example of the classification, we
consider the effective edge model for a fractional topological
insulator for which we calculate the entanglement spectra numerically and show
that all possible predicted phases can be realized.Comment: 11 pages, 7 figures, final versio
- …