405 research outputs found
Lattice spin models for non-Abelian Chiral Spin Liquids
We suggest a class of two-dimensional lattice spin Hamiltonians describing
non-Abelian SU(2) chiral spin liquids - spin-analogues of fractional
non-Abelian quantum Hall states- with gapped bulk and gapless chiral edge
excitations described by the SU(2) Wess-Zumino-Novikov-Witten conformal
field theory. The models are constructed from an array of a generalized
spin- ladders with multi-spin exchange interaction which are coupled by
isolated spins. Such models allow a controllable analytic treatment starting
from the one-dimensional limit and are characterized by a bulk gap and
non-Abelian SU(2) gapless edge excitations.Comment: 7 pages, one figure, replaced by an updated versio
Quantum phase transitions in multileg spin ladders with ring exchange
Four-spin exchange interaction has been raising intriguing questions
regarding the exotic phase transitions it induces in two-dimensional quantum
spin systems. In this context, we investigate the effects of a cyclic four-spin
exchange in the quasi-1D limit by considering a general N-leg spin ladder. We
show by means of a low-energy approach that, depending on its sign, this ring
exchange interaction can engender either a staggered or a uniform dimerization
from the conventional phases of spin ladders. The resulting quantum phase
transition is found to be described by the SU(2)_N conformal field theory. This
result, as well as the fractional value of the central charge at the
transition, is further confirmed by a large-scale numerical study performed by
means of Exact Diagonalization and Density Matrix Renormalization Group
approaches for N \le 4
One-dimensional two-orbital SU(N) ultracold fermionic quantum gases at incommensurate filling: a low-energy approach
We investigate the zero-temperature phase diagram of two-orbital SU(N)
fermionic models at incommensurate filling which are directly relevant to
strontium and ytterbium ultracold atoms loading into a one-dimensional optical
lattice. Using a low-energy approach that takes into account explicitly the
SU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of
freedom is formed for generic interactions. Several phases with one or two
gapless modes are then stabilized which describe the competition between
different density instabilities. In stark contrast to the N=2 case, no dominant
pairing instabilities emerge and the leading superfluid one is rather formed
from bound states of 2N fermions.Comment: 11 pages, 4 figure
Gaplessness of the Gaffnian
We study the Gaffnian trial wavefunction proposed to describe fractional
quantum Hall correlations at Bose filling factor and Fermi filling
. A family of Hamiltonians interpolating between a hard-core
interaction for which the physics is known and a projector whose ground state
is the Gaffnian is studied in detail. We give evidence for the absence of a gap
by using large-scale exact diagonalizations in the spherical geometry. This is
in agreement with recent arguments based on the fact that this wavefunction is
constructed from a non-unitary conformal field theory. By using the cylinder
geometry, we discuss in detail the nature of the underlying minimal model and
we show the appearance of heterotic conformal towers in the edge energy
spectrum where left and right movers are generated by distinct primary
operators.Comment: 11 pages, 5 figure
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