40 research outputs found
The Thermodynamics of Quantum Systems and Generalizations of Zamolodchikov's C-theorem
In this paper we examine the behavior in temperature of the free energy on
quantum systems in an arbitrary number of dimensions. We define from the free
energy a function of the coupling constants and the temperature, which in
the regimes where quantum fluctuations dominate, is a monotonically increasing
function of the temperature. We show that at very low temperatures the system
is controlled by the zero-temperature infrared stable fixed point while at
intermediate temperatures the behavior is that of the unstable fixed point. The
function displays this crossover explicitly. This behavior is reminiscent
of Zamolodchikov's -theorem of field theories in 1+1 dimensions. Our results
are obtained through a thermodynamic renormalization group approach. We find
restrictions on the behavior of the entropy of the system for a
-theorem-type behavior to hold. We illustrate our ideas in the context of a
free massive scalar field theory, the one-dimensional quantum Ising Model and
the quantum Non-linear Sigma Model in two space dimensions. In regimes in which
the classical fluctuations are important the monotonic behavior is absent.Comment: 25 pages, LateX, P-92-10-12
Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases
Using the bosonization approach we study fermionic systems with a nonlinear
dispersion relation in dimension d>2. We explicitly show how the band curvature
gives rise to interaction terms in the bosonic version of the model. Although
these terms are perturbatively irrelevant in relation to the Landau Fermi
liquid fixed point, they become relevant perturbations when instabilities take
place. Using a coherent state path integral technique we built up the effective
action that governs the dynamics of the Fermi surface fluctuations. We consider
the combined effect of fermionic interactions and band curvature on possible
anisotropic phases triggered by negative Landau parameters. In particular we
study in some detail the phase diagram for the isotropic/nematic/hexatic
quantum phase transition.Comment: RevTeX4, 9 pages, 2 eps figures, Final version as appeared in
Phys.Rev.
Hartree-Fock Theory of Hole Stripe States
We report on Hartree-Fock theory results for stripe states of two-dimensional
hole systems in quantum wells grown on GaAs (311)A substrates. We find that the
stripe orientation energy has a rich dependence on hole density, and on
in-plane field magnitude and orientation. Unlike the electron case, the
orientation energy is non-zero for zero in-plane field, and the ground state
orientation can be either parallel or perpendicular to a finite in-plane field.
We predict an orientation reversal transition in in-plane fields applied along
the direction.Comment: 5 pages including 4 figure
Role of disorder in half-filled high Landau levels
We study the effects of disorder on the quantum Hall stripe phases in
half-filled high Landau levels using exact numerical diagonalization. We show
that, in the presence of weak disorder, a compressible, striped charge density
wave, becomes the true ground state. The projected electron density profile
resembles that of a smectic liquid. With increasing disorder strength W, we
find that there exists a critical value, W_c \sim 0.12 e^2/\epsilon l, where a
transition/crossover to an isotropic phase with strong local electron density
fluctuations takes place. The many-body density of states are qualitatively
distinguishable in these two phases and help elucidate the nature of the
transition.Comment: 4 pages, 4 figure
Classical and Quantum Considerations of Two-dimensional Gravity
The two-dimensional theory of gravity describing a graviton-dilaton system is
considered. The graviton-dilaton coupling can be fixed such that the quantum
theory remains free of the conformal anomaly for any conformal dimension of the
coupled matter system, even if the dilaton does not appear as Lagrange
multiplier. Interaction terms are introduced and the system is analyzed and
solutions are given at the classical level and at the quantum level by using
canonical quantization.Comment: 18 page
Electronic Properties of Two-Dimensional Carbon
We present a theoretical description of the electronic properties of graphene
in the presence of disorder, electron-electron interactions, and particle-hole
symmetry breaking. We show that while particle-hole asymmetry, long-range
Coulomb interactions, and extended defects lead to the phenomenon of
self-doping, local defects determine the transport and spectroscopic
properties. Our results explain recent experiments in graphitic devices and
predict new electronic behavior.Comment: 4 pages, 5 figures. The paper was originally submitted on May, 12th,
200
Higher-Spin Theory and Space-Time Metamorphoses
Introductory lectures on higher-spin gauge theory given at 7 Aegean workshop
on non-Einstein theories of gravity. The emphasis is on qualitative features of
the higher-spin gauge theory and peculiarities of its space-time
interpretation. In particular, it is explained that Riemannian geometry cannot
play a fundamental role in the higher-spin gauge theory. The higher-spin
symmetries are argued to occur at ultra high energy scales beyond the Planck
scale. This suggests that the higher-spin gauge theory can help to understand
Quantum Gravity. Various types of higher-spin dualities are briefly discussed.Comment: 37 pages, no figures; V2: references adde
Dynamics of quantum Hall stripes in double-quantum-well systems
The collective modes of stripes in double layer quantum Hall systems are
computed using the time-dependent Hartree-Fock approximation. It is found that,
when the system possesses spontaneous interlayer coherence, there are two
gapless modes, one a phonon associated with broken translational invariance,
the other a pseudospin-wave associated with a broken U(1) symmetry. For large
layer separations the modes disperse weakly for wavevectors perpendicular to
the stripe orientation, indicating the system becomes akin to an array of
weakly coupled one-dimensional XY systems. At higher wavevectors the collective
modes develop a roton minimum associated with a transition out of the coherent
state with further increasing layer separation. A spin wave model of the system
is developed, and it is shown that the collective modes may be described as
those of a system with helimagnetic ordering.Comment: 16 pages including 7 postscript figure
Theory of the Quantum Hall Smectic Phase II: Microscopic Theory
We present a microscopic derivation of the hydrodynamic theory of the Quantum
Hall smectic or stripe phase of a two-dimensional electron gas in a large
magnetic field. The effective action of the low energy is derived here from a
microscopic picture by integrating out high energy excitations with a scale of
the order the cyclotron energy.The remaining low-energy theory can be expressed
in terms of two canonically conjugate sets of degrees of freedom: the
displacement field, that describes the fluctuations of the shapes of the
stripes, and the local charge fluctuations on each stripe.Comment: 20 pages, RevTex, 3 figures, second part of cond-mat/0105448 New and
improved Introduction. Final version as it will appear in Physical Review
Exact eigenstate analysis of finite-frequency conductivity in graphene
We employ the exact eigenstate basis formalism to study electrical
conductivity in graphene, in the presence of short-range diagonal disorder and
inter-valley scattering. We find that for disorder strength, 5, the
density of states is flat. We, then, make connection, using the MRG approach,
with the work of Abrahams \textit{et al.} and find a very good agreement for
disorder strength, = 5. For low disorder strength, = 2, we plot the
energy-resolved current matrix elements squared for different locations of the
Fermi energy from the band centre. We find that the states close to the band
centre are more extended and falls of nearly as as we move away
from the band centre. Further studies of current matrix elements versus
disorder strength suggests a cross-over from weakly localized to a very weakly
localized system. We calculate conductivity using Kubo Greenwood formula and
show that, for low disorder strength, conductivity is in a good qualitative
agreement with the experiments, even for the on-site disorder. The intensity
plots of the eigenstates also reveal clear signatures of puddle formation for
very small carrier concentration. We also make comparison with square lattice
and find that graphene is more easily localized when subject to disorder.Comment: 11 pages,15 figure