961 research outputs found
Topological entanglement entropy relations for multi phase systems with interfaces
We study the change in topological entanglement entropy that occurs when a
two-dimensional system in a topologically ordered phase undergoes a transition
to another such phase due to the formation of a Bose condensate. We also
consider the topological entanglement entropy of systems with domains in
different topological phases, and of phase boundaries between these domains. We
calculate the topological entropy of these interfaces and derive two
fundamental relations between the interface topological entropy and the bulk
topological entropies on both sides of the interface.Comment: 4 pages, 3 figures, 2 tables, revte
Condensate induced transitions between topologically ordered phases
We investigate transitions between topologically ordered phases in two
spatial dimensions induced by the condensation of a bosonic quasiparticle. To
this end, we formulate an extension of the theory of symmetry breaking phase
transitions which applies to phases with topological excitations described by
quantum groups or modular tensor categories. This enables us to deal with
phases whose quasiparticles have non-integer quantum dimensions and obey braid
statistics. Many examples of such phases can be constructed from
two-dimensional rational conformal field theories and we find that there is a
beautiful connection between quantum group symmetry breaking and certain
well-known constructions in conformal field theory, notably the coset
construction, the construction of orbifold models and more general conformal
extensions. Besides the general framework, many representative examples are
worked out in detail.Comment: 27 pages, 3 figures, RevTe
Probing Non-Abelian Statistics with QuasiParticle Interferometry
We examine interferometric experiments in systems that exhibit non-Abelian
braiding statistics, expressing outcomes in terms of the modular S-matrix. In
particular, this result applies to FQH interferometry, and we give a detailed
treatment of the Read-Rezayi states, providing explicit predictions for the
recently observed nu=12/5 plateau.Comment: 5 pages, 1 figure; v2: references added, orientation convention of
the modular S-matrix changed, clarification regarding particle-hole
transformation added; v3: references updated, clarifying changes made to
conform to the version published in PR
Fractional Quantum Hall Hierarchy and the Second Landau Level
We generalize the fractional quantum Hall hierarchy picture to apply to
arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this
to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions
to describe the fractional quantum Hall effect in the second Landau level. The
resulting hierarchy of states, which reproduces the filling fractions of all
observed Hall conductance plateaus in the second Landau level, is characterized
by electron pairing in the ground state and an excitation spectrum that
includes non-Abelian anyons of the Ising type. We propose this as a unifying
picture in which p-wave pairing characterizes the fractional quantum Hall
effect in the second Landau level.Comment: 10 pages; v2: many additional details and discussion included to help
clarify the original results, including a composite fermion type formulation
of some of the states; v3: minor correction
Non-equilibrium noise in the (non-)Abelian fractional quantum Hall effect
We analyse the noise of the edge current of a generic fractional quantum Hall
state in a tunnelling point contact system. We show that the non-symmetrized
noise in the edge current for the system out-of-equilibrium is completely
determined by the noise in the tunnelling current and the Nyquist-Johnson
(equilibrium) noise of the edge current. Simply put, the noise in the
tunnelling current does not simply add up the equilibrium noise of the edge
current. A correction term arises associated with the correlation between the
tunnelling current and the edge current. We show, using a non-equilibrium Ward
identity, that this correction term is determined by the anti-symmetric part of
the noise in the tunnelling current. This leads to a non-equilibrium
fluctuation-dissipation theorem and related expressions for the excess and shot
noise of the noise in the edge current. Our approach makes use of simple
properties of the edge, such as charge conservation and chirality, and applies
to generic constructions of the edge theory which includes edges of non-Abelian
states and edges with multiple charged channels. Two important tools we make
use of are the non-equilibrium Kubo formula and the non-equilibrium Ward
identity. We discuss these identities in the appendix.Comment: 20 pages, 5 figure
Topological Blocking in Quantum Quench Dynamics
We study the non-equilibrium dynamics of quenching through a quantum critical
point in topological systems, focusing on one of their defining features:
ground state degeneracies and associated topological sectors. We present the
notion of 'topological blocking', experienced by the dynamics due to a mismatch
in degeneracies between two phases and we argue that the dynamic evolution of
the quench depends strongly on the topological sector being probed. We
demonstrate this interplay between quench and topology in models stemming from
two extensively studied systems, the transverse Ising chain and the Kitaev
honeycomb model. Through non-local maps of each of these systems, we
effectively study spinless fermionic -wave paired superconductors. Confining
the systems to ring and toroidal geometries, respectively, enables us to
cleanly address degeneracies, subtle issues of fermion occupation and parity,
and mismatches between topological sectors. We show that various features of
the quench, which are related to Kibble-Zurek physics, are sensitive to the
topological sector being probed, in particular, the overlap between the
time-evolved initial ground state and an appropriate low-energy state of the
final Hamiltonian. While most of our study is confined to translationally
invariant systems, where momentum is a convenient quantum number, we briefly
consider the effect of disorder and illustrate how this can influence the
quench in a qualitatively different way depending on the topological sector
considered.Comment: 18 pages, 11 figure
Decoherence of Anyonic Charge in Interferometry Measurements
We examine interferometric measurements of the topological charge of
(non-Abelian) anyons. The target's topological charge is measured from its
effect on the interference of probe particles sent through the interferometer.
We find that superpositions of distinct anyonic charges a and a' in the target
decohere (exponentially in the number of probes particles used) when the probes
have nontrivial monodromy with the charges that may be fused with a to give a'.Comment: 5 pages, 1 figure; v2: reference added, example added, clarifying
changes made to conform to the version published in PR
Abelian homotopy Dijkgraaf-Witten theory
We construct a version of Dijkgraaf-Witten theory based on a compact abelian
Lie group within the formalism of Turaev's homotopy quantum field theory. As an
application we show that the 2+1-dimensional theory based on U(1) classifies
lens spaces up to homotopy type.Comment: 23 pages, 1 figur
Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
We describe a family of phase transitions connecting phases of differing
non-trivial topological order by explicitly constructing Hamiltonians of the
Levin-Wen[PRB 71, 045110] type which can be tuned between two solvable points,
each of which realizes a different topologically ordered phase. We show that
the low-energy degrees of freedom near the phase transition can be mapped onto
those of a Potts model, and we discuss the stability of the resulting phase
diagram to small perturbations about the model. We further explain how the
excitations in the condensed phase are formed from those in the original
topological theory, some of which are split into multiple components by
condensation, and we discuss the implications of our results for understanding
the nature of general achiral topological phases in 2+1 dimensions in terms of
doubled Chern-Simons theories
Interferometric signature of non-Abelian anyons
We consider the tunneling current through a double point-contact Fabry-Pérot interferometer such as used in recent experimental studies of the fractional quantum Hall plateau at filling fraction v=5/2. We compare the predictions of several different models of the state of the electrons at this plateau: the Moore-Read, anti-Pfaffian, SU(2)_2 NAF, K=8 strong pairing, and (3,3,1) states. All of these predict the existence of charge e/4 quasiparticles, but the first three are non-Abelian while the last two are Abelian. We give explicit formulas for the scaling of charge e/2 and charge e/4 quasiparticle contributions to the current as a function of temperature, gate voltage, and distance between the two point contacts for all three models. Based on these, we analyze several possible explanations of two phenomena reported for recent experiments by Willett et al., namely, halving of the period of the observed resistance oscillations with rising temperature and alternation between the same two observed periods at low temperatures as the area of the interference loop is varied with a side gate. We conclude that the most likely explanation is that the observed alternation is due to switching between even and odd numbers of charge e/4 quasiparticles enclosed within the loop as a function of side-gate voltage, which is a clear signature of the presence of non-Abelian anyons. However, there are important features of the data which do not have a simple explanation within this picture. We suggest further experiments which could help rule out some possible scenarios. We make the corresponding predictions for future tunneling and interference experiments at the other observed second Landau level fractional quantum Hall states
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