401 research outputs found
Instantons and the spectral function of electrons in the half-filled Landau level
We calculate the instanton-anti-instanton action in
the gauge theory of the half-filled Landau level. It is found that for a class of interactions between electrons. This means that the instanton-anti-instanton
pairs are confining so that a well defined `charged' composite fermion can
exist. It is also shown that can be used to calculate
the spectral function of electrons from the microscopic theory within a
semiclassical approximation. The resulting spectral function varies as at low
energies.Comment: 13 pages, Plain Tex, MIT-CMT-APR-9
Specific heat and validity of quasiparticle approximation in the half-filled Landau level
We calculate the specific heat of composite fermion system in the half-filled
Landau level. Two different methods are used to examine validity of the
quasiparticle approximation when the two-body interaction is given by (). The singular part of the specific heat
is calculated from the free energy of the gauge field, which is compared with
the specific heat calculated from the quasiparticle approximation via the
singular self-energy correction due to the gauge field fluctuations. It turns
out that two results are in general different and they coincide only for the
case of the Coulomb interaction (). This result supports the fact
that the quasiparticle approximation is valid only for the case of the Coulomb
interaction. It is emphasized that this result is obtained by looking at a
gauge-invariant quantity -- the specific heat.Comment: 8 pages, Revte
Beyond the random phase approximation in the Singwi-Sj\"olander theory of the half-filled Landau level
We study the Chern-Simons system and consider a self-consistent
field theory of the Singwi-Sj\"olander type which goes beyond the random phase
approximation (RPA). By considering the Heisenberg equation of motion for the
longitudinal momentum operator, we are able to show that the zero-frequency
density-density response function vanishes linearly in long wavelength limit
independent of any approximation. From this analysis, we derive a consistency
condition for a decoupling of the equal time density-density and
density-momentum correlation functions. By using the Heisenberg equation of
motion of the Wigner distribution function with a decoupling of the correlation
functions which respects this consistency condition, we calculate the response
functions of the system. In our scheme, we get a density-density
response function which vanishes linearly in the Coulomb case for
zero-frequency in the long wavelength limit. Furthermore, we derive the
compressibility, and the Landau energy as well as the Coulomb energy. These
energies are in better agreement to numerical and exact results, respectively,
than the energies calculated in the RPA.Comment: 9 Revtex pages, 4 eps figures, typos correcte
Spin-Orbit Interaction Enhanced Fractional Quantum Hall States in the Second Landau Level
We study the fractional quantum Hall effect at filling fractions 7/3 and 5/2
in the presence of the spin-orbit interaction, using the exact diagonalization
method and the density matrix renormalization group (DMRG) method in a
spherical geometry. Trial wave functions at these fillings are the Laughlin
state and the Moore-Reed-Pfaffian state. The ground state excitation energy
gaps and pair-correlation functions at fractional filling factor 7/3 and 5/2 in
the second Landau level are calculated. We find that the spin-orbit interaction
stabilizes the fractional quantum Hall states.Comment: 4pages, 4figure
Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes
The pseudopotentials describing the interactions of quasiparticles in
fractional quantum Hall (FQH) states are studied. Rules for the identification
of incompressible quantum fluid ground states are found, based upon the form of
the pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), where
n and p are integers, appear to be the only incompressible states in the
thermodynamic limit, although other FQH hierarchy states occur for finite size
systems. This explains the success of the composite Fermion picture.Comment: RevTeX, 10 pages, 7 EPS figures, submitted fo Phys.Rev.
Spin-singlet hierarchy in the fractional quantum Hall effect
We show that the so-called permanent quantum Hall states are formed by the
integer quantum Hall effects on the Haldane-Rezayi quantum Hall state. Novel
conformal field theory description along with this picture is deduced. The odd
denominator plateaux observed around are the permanent states if the
plateau is the Haldane-Rezayi state. We point out that there is no
such hierarchy on other candidate states for . We propose experiments
to test our prediction.Comment: RevTex,4 pages, v2:typo,one reference adde
Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study
A generalized diffusion Monte Carlo method for solving the many-body
Schr\"odinger equation on curved manifolds is introduced and used to perform a
`fixed-phase' simulation of the fractional quantum Hall effect on the Haldane
sphere. This new method is used to study the effect of Landau level mixing on
the energy gap and the relative stability of spin-polarized and
spin-reversed quasielectron excitations.Comment: 13 pages, Revtex + psfig, figures include
Gauge-invariant response functions of fermions coupled to a gauge field
We study a model of fermions interacting with a gauge field and calculate
gauge-invariant two-particle Green's functions or response functions. The
leading singular contributions from the self-energy correction are found to be
cancelled by those from the vertex correction for small and . As a
result, the remaining contributions are not singular enough to change the
leading order results of the random phase approximation. It is also shown that
the gauge field propagator is not renormalized up to two-loop order. We examine
the resulting gauge-invariant two-particle Green's functions for small and
, but for all ratios of and we conclude that they can
be described by Fermi liquid forms without a diverging effective mass.Comment: Plain Tex, 35 pages, 5 figures available upon request, Revised
Version (Expanded discussion), To be published in Physical Review B 50,
(1994) (December 15 issue
The Haldane-Rezayi Quantum Hall State and Magnetic Flux
We consider the general abelian background configurations for the
Haldane-Rezayi quantum Hall state. We determine the stable configurations to be
the ones with the spontaneous flux of with .
This gives the physical mechanism by which the edge theory of the state becomes
identical to the one for the 331 state. It also provides a new experimental
consequence which can be tested in the enigmatic plateau in a single
layer system.Comment: RevTex, 5 pages, 2 figures. v2:minor corrections. v4: published
version. Discussion on the thermodynamic limit adde
Quantum Boltzmann equation of composite fermions interacting with a gauge field
We derive the quantum Boltzmann equation (QBE) of composite fermions at/near
the state using the non-equilibrium Green's function technique. The
lowest order perturbative correction to the self-energy due to the strong gauge
field fluctuations suggests that there is no well defined
Landau-quasi-particle. Therefore, we cannot assume the existence of the
Landau-quasi-particles {\it a priori} in the derivation of the QBE. Using an
alternative formulation, we derive the QBE for the generalized Fermi surface
displacement which corresponds to the local variation of the chemical potential
in momentum space. {}From this QBE, one can understand in a unified fashion the
Fermi-liquid behaviors of the density-density and the current-current
correlation functions at (in the long wave length and the low
frequency limits) and the singular behavior of the energy gap obtained from the
finite temperature activation behavior of the compressibility near .
Implications of these results to the recent experiments are also discussed.Comment: 44 pages, Plain Tex, 5 figures (ps files) available upon reques
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