86 research outputs found
Is the Composite Fermion a Dirac Particle?
We propose a particle-hole symmetric theory of the Fermi-liquid ground state
of a half-filled Landau level. This theory should be applicable for a Dirac
fermion in the magnetic field at charge neutrality, as well as for the
quantum Hall ground state of nonrelativistic fermions in the
limit of negligible inter-Landau-level mixing. We argue that when particle-hole
symmetry is exact, the composite fermion is a massless Dirac fermion,
characterized by a Berry phase of around the Fermi circle. We write down
a tentative effective field theory of such a fermion and discuss the discrete
symmetries, in particular, . The Dirac composite fermions
interact through a gauge, but non-Chern-Simons, interaction. The particle-hole
conjugate pair of Jain-sequence states at filling factors and
, which in the conventional composite fermion picture
corresponds to integer quantum Hall states with different filling factors,
and , is now mapped to the same half-integer filling factor of
the Dirac composite fermion. The Pfaffian and anti-Pfaffian states are
interpreted as -wave Bardeen-Cooper-Schrieffer paired states of the Dirac
fermion with orbital angular momentum of opposite signs, while -wave pairing
would give rise to a particle-hole symmetric non-Abelian gapped phase. When
particle-hole symmetry is not exact, the Dirac fermion has a -breaking mass. The conventional fermionic Chern-Simons theory is
shown to emerge in the nonrelativistic limit of the massive theory.Comment: 13 pages; v2: added discussion of experimental signatures, Kohn's
theorem; v3: typo fixed, published versio
Hydrodynamics on the lowest Landau level
Using the recently developed approach to quantum Hall physics based on
Newton-Cartan geometry, we consider the hydrodynamics of an interacting system
on the lowest Landau level. We rephrase the non-relativistic fluid equations of
motion in a manner that manifests the spacetime diffeomorphism invariance of
the underlying theory. In the massless (or lowest Landau level) limit, the
fluid obeys a force-free constraint which fixes the charge current. An entropy
current analysis further constrains the energy response, determining four
transverse response functions in terms of only two: an energy magnetization and
a thermal Hall conductivity. Kubo formulas are presented for all transport
coefficients and constraints from Weyl invariance derived. We also present a
number of Streda-type formulas for the equilibrium response to external
electric, magnetic and gravitational fields
Bimetric Theory of Fractional Quantum Hall States
We present a bimetric low-energy effective theory of fractional quantum Hall
(FQH) states that describes the topological properties and a gapped collective
excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist
of a topological Chern-Simons action, coupled to a symmetric rank two tensor,
and an action \`a la bimetric gravity, describing the gapped dynamics of the
spin- GMP mode. The theory is formulated in curved ambient space and is
spatially covariant, which allows to restrict the form of the effective action
and the values of phenomenological coefficients. Using the bimetric theory we
calculate the projected static structure factor up to the order in the
momentum expansion. To provide further support for the theory, we derive the
long wave limit of the GMP algebra, the dispersion relation of the GMP mode,
and the Hall viscosity of FQH states. We also comment on the possible
applications to fractional Chern insulators, where closely related structures
arise. Finally, it is shown that the familiar FQH observables acquire a curious
geometric interpretation within the bimetric formalism.Comment: 14 pages, v2: Acknowledgments updated, v3: A few presentation
improvements, Published versio
Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum
We study the spontaneous parity breaking and generating of Hall viscosity and
angular momentum in holographic p+ip model, which can describe strongly-coupled
chiral superfluid states in many quantum systems. The dual gravity theory, an
SU(2) gauge field minimally coupled to Einstein gravity, is parity-invariant
but allows a black hole solution with vector hair corresponding to a
parity-broken superfluid state. We show that this state possesses a
non-vanishing parity-odd transport coefficient -- Hall viscosity -- and an
angular momentum density. We first develop an analytic method to solve this
model near the critical regime and to take back-reactions into account. Then we
solve the equation for the tensor mode fluctuations and obtain the expression
for Hall viscosity via Kubo formula. We also show that a non-vanishing angular
momentum density can be obtained through the vector mode fluctuations and the
corresponding boundary action. We give analytic results of both Hall viscosity
and angular momentum density near the critical regime in terms of physical
parameters. The near-critical behavior of Hall viscosity is different from that
obtained from a gravitational Chern-Simons model. We find that the magnitude of
Hall viscosity to angular momentum density ratio is numerically consistent with
being equal to 1/2 at large SU(2) coupling corresponding to the probe limit, in
agreement with previous results obtained for various quantum fluid systems and
from effective theory approaches. In addition, we find the shear viscosity to
entropy density ratio remains above the universal bound.Comment: 55 pages, 1 figure. Version 2: angular momentum calculation revised;
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