27 research outputs found
On the Absence of Cross-Confinement for Dynamically Generated Multi-Chern-Simons Theories
We show that when the induced parity breaking part of the effective action
for the low-momentum region of U(1) x ... x U(1) Maxwell gauge field theory
with massive fermions in 3 dimensions is coupled to a \phi^4 scalar field
theory, it is not possible to eliminate the screening of the long-range Coulomb
interactions and get external charges confined in the broken Higgs phase. This
result is valid for non-zero temperature as well.Comment: 7 pages, LaTe
A non-abelian spin-liquid in a spin-1 quantum magnet
We study a time-reversal invariant non-abelian spin-liquid state in an symmetric spin quantum magnet on a triangular lattice. The
spin-liquid is obtained by quantum disordering a non-collinear nematic state.
We show that such a spin-liquid cannot be obtained by the standard projective
construction for spin-liquids. We also study phase transition between the
spin-liquid and the non-collinear nematic state and show that it cannot be
described within Landau-Ginzburg- Wilson paradigm.Comment: 4.25 pages, 1 figur
Non-locality of non-Abelian anyons
Topological systems, such as fractional quantum Hall liquids, promise to
successfully combat environmental decoherence while performing quantum
computation. These highly correlated systems can support non-Abelian anyonic
quasiparticles that can encode exotic entangled states. To reveal the non-local
character of these encoded states we demonstrate the violation of suitable Bell
inequalities. We provide an explicit recipe for the preparation, manipulation
and measurement of the desired correlations for a large class of topological
models. This proposal gives an operational measure of non-locality for anyonic
states and it opens up the possibility to violate the Bell inequalities in
quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure
Defect mediated melting and the breaking of quantum double symmetries
In this paper, we apply the method of breaking quantum double symmetries to
some cases of defect mediated melting. The formalism allows for a systematic
classification of possible defect condensates and the subsequent confinement
and/or liberation of other degrees of freedom. We also show that the breaking
of a double symmetry may well involve a (partial) restoration of an original
symmetry. A detailed analysis of a number of simple but representative examples
is given, where we focus on systems with global internal and external (space)
symmetries. We start by rephrasing some of the well known cases involving an
Abelian defect condensate, such as the Kosterlitz-Thouless transition and
one-dimensional melting, in our language. Then we proceed to the non-Abelian
case of a hexagonal crystal, where the hexatic phase is realized if
translational defects condense in a particular rotationally invariant state.
Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference
From spin to anyon notation: The XXZ Heisenberg model as a (or ) anyon chain
We discuss a relationship between certain one-dimensional quantum spin chains
and anyon chains. In particular we show how the XXZ Heisenberg chain is
realised as a (alternately ) anyon model. We find the
difference between the models lie primarily in choice of boundary condition.Comment: 13 page
Qudit surface codes and gauge theory with finite cyclic groups
Surface codes describe quantum memory stored as a global property of
interacting spins on a surface. The state space is fixed by a complete set of
quasi-local stabilizer operators and the code dimension depends on the first
homology group of the surface complex. These code states can be actively
stabilized by measurements or, alternatively, can be prepared by cooling to the
ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2
(qubit) lattices, such ground states have been proposed as topologically
protected memory for qubits. We extend these constructions to lattices or more
generally cell complexes with qudits, either of prime level or of level
for prime and , and therefore under tensor
decomposition, to arbitrary finite levels. The Hamiltonian describes an exact
gauge theory whose excitations
correspond to abelian anyons. We provide protocols for qudit storage and
retrieval and propose an interferometric verification of topological order by
measuring quasi-particle statistics.Comment: 26 pages, 5 figure
Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator
Recently a pair of experiments demonstrated a simulation of Abelian anyons in
a spin network of single photons. The experiments were based on an Abelian
discrete gauge theory spin lattice model of Kitaev. Here we describe how to use
linear optics and single photons to simulate non-Abelian anyons. The scheme
makes use of joint qutrit-qubit encoding of the spins and the resources
required are three pairs of parametric down converted photons and 14 beam
splitters.Comment: 13 pages, 5 figures. Several references added in v
The modular S-matrix as order parameter for topological phase transitions
We study topological phase transitions in discrete gauge theories in two
spatial dimensions induced by the formation of a Bose condensate. We analyse a
general class of euclidean lattice actions for these theories which contain one
coupling constant for each conjugacy class of the gauge group. To probe the
phase structure we use a complete set of open and closed anyonic string
operators. The open strings allow one to determine the particle content of the
condensate, whereas the closed strings enable us to determine the matrix
elements of the modular -matrix, also in the broken phase. From the measured
broken -matrix we may read off the sectors that split or get identified in
the broken phase, as well as the sectors that are confined. In this sense the
modular -matrix can be employed as a matrix valued non-local order parameter
from which the low-energy effective theories that occur in different regions of
parameter space can be fully determined.
To verify our predictions we studied a non-abelian anyon model based on the
quaternion group of order eight by Monte Carlo simulation. We
probe part of the phase diagram for the pure gauge theory and find a variety of
phases with magnetic condensates leading to various forms of (partial)
confinement in complete agreement with the algebraic breaking analysis. Also
the order of various transitions is established.Comment: 37 page
Non-Abelian Chern-Simons models with discrete gauge groups on a lattice
We construct the local Hamiltonian description of the Chern-Simons theory
with discrete non-Abelian gauge group on a lattice. We show that the theory is
fully determined by the phase factors associated with gauge transformations and
classify all possible non-equivalent phase factors. We also construct the gauge
invariant electric field operators that move fluxons around and
create/anihilate them. We compute the resulting braiding properties of the
fluxons. We apply our general results to the simplest class of non-Abelian
groups, dihedral groups D_n.Comment: 16 pages, 7 figure
Fourier transform and the Verlinde formula for the quantum double of a finite group
A Fourier transform S is defined for the quantum double D(G) of a finite
group G. Acting on characters of D(G), S and the central ribbon element of D(G)
generate a unitary matrix representation of the group SL(2,Z). The characters
form a ring over the integers under both the algebra multiplication and its
dual, with the latter encoding the fusion rules of D(G). The Fourier transform
relates the two ring structures. We use this to give a particularly short proof
of the Verlinde formula for the fusion coefficients.Comment: 15 pages, small errors corrected and references added, version to
appear in Journal of Physics