10 research outputs found
Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields
We study edge dynamics in the presence of interlayer tunneling, parallel
magnetic field, and various types of disorder for two infinite sequences of
quantum Hall states in symmetric bilayers. These sequences begin with the 110
and 331 Halperin states and include their fractional descendants at lower
filling factors; the former is easily realized experimentally while the latter
is a candidate for the experimentally observed quantum Hall state at a total
filling factor of 1/2 in bilayers. We discuss the experimentally interesting
observables that involve just one chiral edge of the sample and the correlation
functions needed for computing them. We present several methods for obtaining
exact results in the presence of interactions and disorder which rely on the
chiral character of the system. Of particular interest are our results on the
331 state which suggest that a time-resolved measurement at the edge can be
used to discriminate between the 331 and Pfaffian scenarios for the observed
quantum Hall state at filling factor 1/2 in realistic double-layer systems.Comment: revtex+epsf; two-up postscript at
http://www.sns.ias.edu/~leonid/ntwoup.p
Activation Energy in a Quantum Hall Ferromagnet and Non-Hartree-Fock Skyrmions
The energy of Skyrmions is calculated with the help of a technique based on
the excitonic representation: the basic set of one-exciton states is used for
the perturbation-theory formalism instead of the basic set of one-particle
states. We use the approach, at which a skyrmion-type excitation (at zero Lande
factor) is considered as a smooth non-uniform rotation in the 3D spin space.
The result within the framework of an excitonically diagonalized part of the
Coulomb Hamiltonian can be obtained by any ratio [where is the typical Coulomb
energy ( being the magnetic length); is the cyclotron
frequency], and the Landau-level mixing is thereby taken into account. In
parallel with this, the result is also found exactly, to second order in terms
of the (if supposing to be small) with use of the
total Hamiltonian. When extrapolated to the region , our
calculations show that the skyrmion gap becomes substantially reduced in
comparison with the Hartree-Fock calculations. This fact brings the theory
essentially closer to the available experimental data.Comment: 14 pages, 1 figure. to appear in Phys. Rev. B, Vol. 65 (Numbers ~
19-22), 200
Three dimensional resonating valence bond liquids and their excitations
We show that there are two types of RVB liquid phases present in
three-dimensional quantum dimer models, corresponding to the deconfining phases
of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite
cubic lattice and is the generalization of the critical point in the square
lattice quantum dimer model found originally by Rokhsar and Kivelson. The
latter exists on the non-bipartite face-centred cubic lattice and generalizes
the RVB phase found earlier by us on the triangular lattice. We discuss the
excitation spectrum and the nature of the ordering in both cases. Both phases
exhibit gapped spinons. In the U(1) case we find a collective, linearly
dispersing, transverse excitation, which is the photon of the low energy
Maxwell Lagrangian and we identify the ordering as quantum order in Wen's
sense. In the Z_2 case all collective excitations are gapped and, as in d=2,
the low energy description of this topologically ordered state is the purely
topological BF action. As a byproduct of this analysis, we unearth a further
gapless excitation, the pi0n, in the square lattice quantum dimer model at its
critical point.Comment: 9 pages, 2 figure
Interplay of quantum and thermal fluctuations in a frustrated magnet
We demonstrate the presence of an extended critical phase in the transverse
field Ising magnet on the triangular lattice, in a regime where both thermal
and quantum fluctuations are important. We map out a complete phase diagram by
means of quantum Monte Carlo simulations, and find that the critical phase is
the result of thermal fluctuations destabilising an order established by the
quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions
from the paramagnet on one hand and the quantum-fluctuation driven
three-sublattice ordered phase on the other. Our work provides further evidence
that the zero temperature quantum phase transition is in the 3d XY universality
class.Comment: 9 pages, revtex
Hamiltonian Theory of the FQHE: Conserving Approximation for Incompressible Fractions
A microscopic Hamiltonian theory of the FQHE developed by Shankar and the
present author based on the fermionic Chern-Simons approach has recently been
quite successful in calculating gaps and finite tempertature properties in
Fractional Quantum Hall states. Initially proposed as a small- theory, it
was subsequently extended by Shankar to form an algebraically consistent theory
for all in the lowest Landau level. Such a theory is amenable to a
conserving approximation in which the constraints have vanishing correlators
and decouple from physical response functions. Properties of the incompressible
fractions are explored in this conserving approximation, including the
magnetoexciton dispersions and the evolution of the small- structure factor
as \nu\to\half. Finally, a formalism capable of dealing with a nonuniform
ground state charge density is developed and used to show how the correct
fractional value of the quasiparticle charge emerges from the theory.Comment: 15 pages, 2 eps figure
Fractionalization patterns in strongly correlated electron systems: Spin-charge separation and beyond
We discuss possible patterns of electron fractionalization in strongly
interacting electron systems. A popular possibility is one in which the charge
of the electron has been liberated from its Fermi statistics. Such a
fractionalized phase contains in it the seed of superconductivity. Another
possibility occurs when the spin of the electron, rather than its charge, is
liberated from its Fermi statistics. Such a phase contains in it the seed of
magnetism, rather than superconductivity. We consider models in which both of
these phases occur and study possible phase transitions between them. We
describe other fractionalized phases, distinct from these, in which fractions
of the electron themselves fractionalize, and discuss the topological
characterization of such phases. These ideas are illustrated with specific
models of p-wave superconductors, Kondo lattices, and coexistence between
d-wave superconductivity and antiferromagnetism.Comment: 28 pages, 11 fig
Non-zero temperature transport near quantum critical points
We describe the nature of charge transport at non-zero temperatures ()
above the two-dimensional () superfluid-insulator quantum critical point. We
argue that the transport is characterized by inelastic collisions among
thermally excited carriers at a rate of order . This implies that
the transport at frequencies is in the hydrodynamic,
collision-dominated (or `incoherent') regime, while is
the collisionless (or `phase-coherent') regime. The conductivity is argued to
be times a non-trivial universal scaling function of , and not independent of , as has been previously
claimed, or implicitly assumed. The experimentally measured d.c. conductivity
is the hydrodynamic limit of this function, and is a
universal number times , even though the transport is incoherent.
Previous work determined the conductivity by incorrectly assuming it was also
equal to the collisionless limit of the scaling
function, which actually describes phase-coherent transport with a conductivity
given by a different universal number times . We provide the first
computation of the universal d.c. conductivity in a disorder-free boson model,
along with explicit crossover functions, using a quantum Boltzmann equation and
an expansion in . The case of spin transport near quantum
critical points in antiferromagnets is also discussed. Similar ideas should
apply to the transitions in quantum Hall systems and to metal-insulator
transitions. We suggest experimental tests of our picture and speculate on a
new route to self-duality at two-dimensional quantum critical points.Comment: Feedback incorporated into numerous clarifying remarks; additional
appendix discusses relationship to transport in dissipative quantum mechanics
and quantum Hall edge state tunnelling problems, stimulated by discussions
with E. Fradki
Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
In this paper, we review theoretical and experimental research on rare region
effects at quantum phase transitions in disordered itinerant electron systems.
After summarizing a few basic concepts about phase transitions in the presence
of quenched randomness, we introduce the idea of rare regions and discuss their
importance. We then analyze in detail the different phenomena that can arise at
magnetic quantum phase transitions in disordered metals, including quantum
Griffiths singularities, smeared phase transitions, and cluster-glass
formation. For each scenario, we discuss the resulting phase diagram and
summarize the behavior of various observables. We then review several recent
experiments that provide examples of these rare region phenomena. We conclude
by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative
Ising chain fixed, references added, v3: final version as publishe