7,236 research outputs found
Toward a Conformal Field Theory for the Quantum Hall Effect
An effective Hamiltonian for the study of the quantum Hall effect is
proposed. This Hamiltonian, which includes a ``current-current" interaction has
the form of a Hamiltonian for a conformal field theory in the large limit.
An order parameter is constructed from which the Hamiltonian may be derived.
This order parameter may be viewed as either a collective coordinate for a
system of charged particles in a strong magnetic field; or as a field of
spins associated with the cyclotron motion of these particles.Comment: 14 pg
The Quantum Hall Effect: Unified Scaling Theory and Quasi-particles at the Edge
We address two fundamental issues in the physics of the quantum Hall effect:
a unified description of scaling behavior of conductances in the integral and
fractional regimes, and a quasi-particle formulation of the chiral Luttinger
Liquids that describe the dynamics of edge excitations in the fractional
regime.Comment: 11 pages, LateX, 2 figures (not included, available from the
authors), to be published in Proceedings of the International Summer School
on Strongly Correlated Electron Systems, Lajos Kossuth University, Debrecen,
Hungary, Sept 199
Holographic fermions in external magnetic fields
We study the Fermi level structure of 2+1-dimensional strongly interacting
electron systems in external magnetic field using the AdS/CFT correspondence.
The gravity dual of a finite density fermion system is a Dirac field in the
background of the dyonic AdS-Reissner-Nordstrom black hole. In the probe limit
the magnetic system can be reduced to the non-magnetic one, with
Landau-quantized momenta and rescaled thermodynamical variables. We find that
at strong enough magnetic fields, the Fermi surface vanishes and the
quasiparticle is lost either through a crossover to conformal regime or through
a phase transition to an unstable Fermi surface. In the latter case, the
vanishing Fermi velocity at the critical magnetic field triggers the non-Fermi
liquid regime with unstable quasiparticles and a change in transport properties
of the system. We associate it with a metal-"strange metal" phase transition.
Next we compute the DC Hall and longitudinal conductivities using the
gravity-dressed fermion propagators. For dual fermions with a large charge,
many different Fermi surfaces contribute and the Hall conductivity is quantized
as expected for integer Quantum Hall Effect (QHE). At strong magnetic fields,
as additional Fermi surfaces open up, new plateaus typical for the fractional
QHE appear. The somewhat irregular pattern in the length of fractional QHE
plateaus resemble the outcomes of experiments on thin graphite in a strong
magnetic field. Finally, motivated by the absence of the sign problem in
holography, we suggest a lattice approach to the AdS calculations of finite
density systems.Comment: 34 pages, 14 figure
Strong Coupling Fixed Points of Current Interactions and Disordered Fermions in 2D
The all-orders beta function is used to study disordered Dirac fermions in
2D. The generic strong coupling fixed `points' of anisotropic current-current
interactions at large distances are actually isotropic manifolds corresponding
to subalgebras of the maximal current algebra at short distances. The IR
theories are argued to be current algebra cosets. We illustrate this with the
simple example of anisotropic su(2), which is the physics of
Kosterlitz-Thouless transitions. We work out the phase diagram for the
Chalker-Coddington network model which is in the universality class of the
integer Quantum Hall transition. One massless phase is in the universality
class of dense polymers.Comment: published version (Phys. Rev. B
Physical principles underlying the quantum Hall effect
In this contribution, we present an introduction to the physical principles
underlying the quantum Hall effect. The field theoretic approach to the
integral and fractional effect is sketched, with some emphasis on the mechanism
of electromagnetic gauge anomaly cancellation by chiral degrees of freedom
living on the edge of the sample. Applications of this formalism to the design
and theoretical interpretation of interference experiments are outlined.Comment: 20 pages, 8 figures; small corrections, replaced with published
versio
Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
We show that Horava-Lifshitz gravity theory can be employed as a covariant
framework to build an effective field theory for the fractional quantum Hall
effect that respects all the spacetime symmetries such as non-relativistic
diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge
symmetry. The key to this formalism is a set of correspondence relations that
maps all the field degrees of freedom in the Horava-Lifshitz gravity theory to
external background (source) fields among others in the effective action of the
quantum Hall effect, according to their symmetry transformation properties. We
originally derive the map as a holographic dictionary, but its form is
independent of the existence of holographic duality. This paves the way for the
application of Horava-Lifshitz holography on fractional quantum Hall effect.
Using the simplest holographic Chern-Simons model, we compute the low energy
effective action at leading orders and show that it captures universal
electromagnetic and geometric properties of quantum Hall states, including the
Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We
identify the shift function in Horava-Lifshitz gravity theory as minus of
guiding center velocity and conjugate to guiding center momentum. This enables
us to distinguish guiding center angular momentum density from the internal
one, which is the sum of Landau orbit spin and intrinsic (topological) spin of
the composite particles. Our effective action shows that Hall viscosity is
minus half of the internal angular momentum density and proportional to Wen-Zee
shift, and Hall bulk viscosity is half of the guiding center angular momentum
density.Comment: 69 page
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
A twisted conformal field theory description of dissipative quantum mechanics
We show how the recently proposed CFT for a bilayer Quantum Hall system at
filling nu=m/pm+2, the Twisted Model (TM), is equivalent to the system of two
massless scalar bosons with a magnetic boundary interaction as introduced in
Nucl. Phys. B443 (1995) 444, at the so called magic points. We are then able to
describe, within such a framework, the dissipative quantum mechanics of a
particle confined to a plane and subject to an external magnetic field normal
to it. Such an analogy is further developed in terms of the TM boundary states,
by describing the interaction between an impurity with a Hall system.Comment: 13 pages, no figures, Late
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