2,996 research outputs found
A mean field approach for string condensed states
We describe a mean field technique for quantum string (or dimer) models.
Unlike traditional mean field approaches, the method is general enough to
include string condensed phases in addition to the usual symmetry breaking
phases. Thus, it can be used to study phases and phases transitions beyond
Landau's symmetry breaking paradigm. We demonstrate the technique with a simple
example: the spin-1 XXZ model on the Kagome lattice. The mean field calculation
predicts a number of phases and phase transitions, including a z=2 deconfined
quantum critical point.Comment: 10 pages + appendix, 15 figure
Fidelity and quantum phase transitions
It is shown that the fidelity, a basic notion of quantum information science,
may be used to characterize quantum phase transitions, regardless of what type
of internal order is present in quantum many-body states. If the fidelity of
two given states vanishes, then there are two cases: (1) they are in the same
phase if the distinguishability results from irrelevant local information; or
(2) they are in different phases if the distinguishability results from
relevant long-distance information. The different effects of irrelevant and
relevant information are quantified, which allows us to identify unstable and
stable fixed points (in the sense of renormalization group theory). A physical
implication of our results is the occurrence of the orthogonality catastrophe
near the transition points.Comment: 5 pages, 2 figure
Minimal Models for a Superconductor-Insulator Conformal Quantum Phase Transition
Conformal field theories do not only classify 2D classical critical behavior
but they also govern a certain class of 2D quantum critical behavior. In this
latter case it is the ground state wave functional of the quantum theory that
is conformally invariant, rather than the classical action. We show that the
superconducting-insulating (SI) quantum phase transition in 2D Josephson
junction arrays (JJAs) is a (doubled) Gaussian conformal quantum critical
point. The quantum action describing this system is a doubled
Maxwell-Chern-Simons model in the strong coupling limit. We also argue that the
SI quantum transitions in frustrated JJAs realize the other possible
universality classes of conformal quantum critical behavior, corresponding to
the unitary minimal models at central charge .Comment: 4 pages, no figure
Spin- generalization of fractional exclusion statistics
We study fractional exclusion statistics for quantum systems with SU(2)
symmetry (arbitrary spin ), by generalizing the thermodynamic equations with
squeezed strings proposed by Ha and Haldane. The bare hole distributions as
well as the statistical interaction defined by an infinite-dimensional matrix
specify the universality class. It is shown that the system is described by the
level- WZW model and has a close relationship to non-abelian fractional
quantum Hall states. As a low-energy effective theory, the sector of {\it
massless} Z parafermions is extracted, whose statistical interaction is
given by a finite-dimensional matrix.Comment: 11pages, REVTE
Superconducting Topological Fluids in Josephson Junction Arrays
We argue that the frustrated Josephson junction arrays may support a
topologically ordered superconducting ground state, characterized by a
non-trivial ground state degeneracy on the torus. This superconducting quantum
fluid provides an explicit example of a system in which superconductivity
arises from a topological mechanism rather than from the usual Landau-Ginzburg
mechanism.Comment: 4 page
Topological Quantum Phase Transitions in Topological Superconductors
In this paper we show that BF topological superconductors (insulators) exibit
phase transitions between different topologically ordered phases characterized
by different ground state degeneracy on manifold with non-trivial topology.
These phase transitions are induced by the condensation (or lack of) of
topological defects. We concentrate on the (2+1)-dimensional case where the BF
model reduce to a mixed Chern-Simons term and we show that the superconducting
phase has a ground state degeneracy and not . When the symmetry is
, namely when both gauge fields are compact, this model is
not equivalent to the sum of two Chern-Simons term with opposite chirality,
even if naively diagonalizable. This is due to the fact that U(1) symmetry
requires an ultraviolet regularization that make the diagonalization
impossible. This can be clearly seen using a lattice regularization, where the
gauge fields become angular variables. Moreover we will show that the phase in
which both gauge fields are compact is not allowed dynamically.Comment: 5 pages, no figure
Quasi-Particle Tunneling in Anti-Pfaffian Quantum Hall State
We study tunneling phenomena at the edge of the anti-Pfaffian quantum Hall
state at the filling factor . The edge current in a single
point-contact is considered. We focus on nonlinear behavior of two-terminal
conductance with the increase in negative split-gate voltage. Expecting the
appearance of the intermediate conductance plateau we calculate the value of
its conductance by using the renormalization group (RG) analysis. Further, we
show that non-perturbative quasi-particle tunneling is effectively described as
perturbative electron tunneling by the instanton method. The two-terminals
conductance is written as a function of the gate voltage. The obtained results
enable us to distinguish the anti-Pfaffian state from the Pfaffian state
experimentally.Comment: 5 pages, 4 figure
Non-Abelian Anyons and Topological Quantum Computation
Topological quantum computation has recently emerged as one of the most
exciting approaches to constructing a fault-tolerant quantum computer. The
proposal relies on the existence of topological states of matter whose
quasiparticle excitations are neither bosons nor fermions, but are particles
known as {\it Non-Abelian anyons}, meaning that they obey {\it non-Abelian
braiding statistics}. Quantum information is stored in states with multiple
quasiparticles, which have a topological degeneracy. The unitary gate
operations which are necessary for quantum computation are carried out by
braiding quasiparticles, and then measuring the multi-quasiparticle states. The
fault-tolerance of a topological quantum computer arises from the non-local
encoding of the states of the quasiparticles, which makes them immune to errors
caused by local perturbations. To date, the only such topological states
thought to have been found in nature are fractional quantum Hall states, most
prominently the \nu=5/2 state, although several other prospective candidates
have been proposed in systems as disparate as ultra-cold atoms in optical
lattices and thin film superconductors. In this review article, we describe
current research in this field, focusing on the general theoretical concepts of
non-Abelian statistics as it relates to topological quantum computation, on
understanding non-Abelian quantum Hall states, on proposed experiments to
detect non-Abelian anyons, and on proposed architectures for a topological
quantum computer. We address both the mathematical underpinnings of topological
quantum computation and the physics of the subject using the \nu=5/2 fractional
quantum Hall state as the archetype of a non-Abelian topological state enabling
fault-tolerant quantum computation.Comment: Final Accepted form for RM
Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in
the limit of strong easy-axis exchange anisotropy. We find, using only standard
techniques of degenerate perturbation theory, that the model has a U(1) gauge
symmetry generated by certain local rotations about the z-axis in spin space.
Upon addition of an extra local interaction in this and a related model with
spins on a three-dimensional network of corner-sharing octahedra, we can write
down the exact ground state wavefunction with no further approximations. Using
the properties of the soluble point we show that these models enter the U(1)
spin liquid phase, a novel fractionalized spin liquid with an emergent U(1)
gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1)
``electric'' gauge charge, a gapped topological point defect or ``magnetic''
monopole, and a gapless ``photon,'' which in spin language is a gapless,
linearly dispersing S^z = 0 collective mode. There are power-law spin
correlations with a nontrivial angular dependence, as well as novel U(1)
topological order. This state is stable to ALL zero-temperature perturbations
and exists over a finite extent of the phase diagram. Using a convenient
lattice version of electric-magnetic duality, we develop the effective
description of the U(1) spin liquid and the adjacent soluble point in terms of
Gaussian quantum electrodynamics and calculate a few of the universal
properties. The resulting picture is confirmed by our numerical analysis of the
soluble point wavefunction. Finally, we briefly discuss the prospects for
understanding this physics in a wider range of models and for making contact
with experiments.Comment: 22 pages, 14 figures. Further minor changes. To appear in Phys. Rev.
Coulomb Correlations and Pseudo-gap Effects in a Pre-formed Pair Model for the Cuprates
We extend previous work on pre-formed pair models of superconductivity to
incorporate Coulomb correlation effects. For neutral systems, these models have
provided a useful scheme which interpolates between BCS and Bose Einstein
condensation with increasing coupling and thereby describes some aspects of
pseudo-gap phenomena. However, charge fluctuations (via the plasmon,
) significantly modify the collective modes and therefore the
interpolation behavior. We discuss the resulting behavior of the pseudo-gap and
thermodynamic quantities such as , and as a function of
.Comment: 4 pages RevTeX, 3 ps figures included (Submitted to Physical Review B
August 27, 1996
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