20,572 research outputs found
Renyi entropies of free bosons on the torus and holography
We analytically evaluate the Renyi entropies for the two dimensional free
boson CFT. The CFT is considered to be compactified on a circle and at finite
temperature. The Renyi entropies S_n are evaluated for a single interval using
the two point function of bosonic twist fields on a torus. For the case of the
compact boson, the sum over the classical saddle points results in the
Riemann-Siegel theta function associated with the A_{n-1} lattice. We then
study the Renyi entropies in the decompactification regime. We show that in the
limit when the size of the interval becomes the size of the spatial circle, the
entanglement entropy reduces to the thermal entropy of free bosons on a circle.
We then set up a systematic high temperature expansion of the Renyi entropies
and evaluate the finite size corrections for free bosons. Finally we compare
these finite size corrections both for the free boson CFT and the free fermion
CFT with the one-loop corrections obtained from bulk three dimensional
handlebody spacetimes which have higher genus Riemann surfaces as its boundary.
One-loop corrections in these geometries are entirely determined by quantum
numbers of the excitations present in the bulk. This implies that the leading
finite size corrections contributions from one-loop determinants of the
Chern-Simons gauge field and the Dirac field in the dual geometry should
reproduce that of the free boson and the free fermion CFT respectively. By
evaluating these corrections both in the bulk and in the CFT explicitly we show
that this expectation is indeed true.Comment: Published version. 56 pages. 6 figures. Argument for the agreement of
the leading finite size corrections evaluated from CFT and gravity has been
adde
The Deconfinement Transition in SO(3) Gauge Theory
The SO(3) lattice gauge theory with a Villain form of action was investigated
by Monte Carlo techniques on asymmetric lattices with Nt = 2 and 4, where Nt is
the number of sites in the temporal extent. Unlike the results for higher Nt,
only one transition of second order was found for Nt = 2 . An extended action
with an irrelevant term to suppress Z_2 monopoles enabled us to get a better
view of the deconfinement transition as the effects of bulk transition could be
suppressed as well. Although the action has no global Z_2 symmetry for the
SO(3) theory, unlike the SU(2) theory at finite temperature, our study revealed
a second order deconfinement transition, with properties similar to the
deconfinement transition of SU(2).Comment: 19 pages latex, incl. figure
Supersymmetry of classical solutions in Chern-Simons higher spin supergravity
We construct and study classical solutions in Chern-Simons supergravity based
on the superalgebra sl(N|N-1). The algebra for the N=3 case is written down
explicitly using the fact that it arises as the global part of the super
conformal W_3 superalgebra. For this case we construct new classical solutions
and study their supersymmetry. Using the algebra we write down the Killing
spinor equations and explicitly construct the Killing spinor for conical
defects and black holes in this theory. We show that for the general sl(N|N-1)
theory the condition for the periodicity of the Killing spinor can be written
in terms of the products of the odd roots of the super algebra and the
eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of
a given background can be stated in terms of gauge invariant and well defined
physical observables of the Chern-Simons theory. We then show that for N\geq 4,
the sl(N|N-1) theory admits smooth supersymmetric conical defects.Comment: 40 pages, includes discussion of conical defects for N\geq 4, typos
corrected and presentation improve
Black holes in higher spin supergravity
We study black hole solutions in Chern-Simons higher spin supergravity based
on the superalgebra sl(3|2). These black hole solutions have a U(1) gauge field
and a spin 2 hair in addition to the spin 3 hair. These additional fields
correspond to the R-symmetry charges of the supergroup sl(3|2). Using the
relation between the bulk field equations and the Ward identities of a CFT with
N=2 super-W_3 symmetry, we identify the bulk charges and chemical potentials
with those of the boundary CFT. From these identifications we see that a
suitable set of variables to study this black hole is in terms of the charges
present in three decoupled bosonic sub-algebras of the N=2 super-W_3 algebra.
The entropy and the partition function of these R-charged black holes are then
evaluated in terms of the charges of the bulk theory as well as in terms of its
chemical potentials. We then compute the partition function in the dual CFT and
find exact agreement with the bulk partition function.Comment: 27 pages. Published versio
Relation between dispersion lines and conductance of telescoped armchair double-wall nanotubes analyzed using perturbation formulas and first-principles calculations
The Landauer's formula conductance of the telescoped armchair nanotubes is
calculated with the Hamiltonian defined by first-principles calculations
(SIESTA code). Herein, partially extracting the inner tube from the outer tube
is called 'telescoping'. It shows a rapid oscillation superposed on a slow
oscillation as a function of discrete overlap length with an integer
variable and the lattice constant . Considering the interlayer
Hamiltonian as a perturbation, we obtain the approximate formula of the
amplitude of the slow oscillation as where is
the effective interlayer interaction and is the band split
without interlayer interaction. The approximate formula is related to the
Thouless number of the dispersion lines.Comment: 9 figure
Finite Conductivity in Mesoscopic Hall Bars of Inverted InAs/GaSb Quantum Wells
We have studied experimentally the low temperature conductivity of mesoscopic
size InAs/GaSb quantum well Hall bar devices in the inverted regime. Using a
pair of electrostatic gates we were able to move the Fermi level into the
electron-hole hybridization state, and observe a mini gap. Temperature
dependence of the conductivity in the gap shows residual conductivity, which
can be consistently explained by the contributions from the free as well as the
hybridized carriers in the presence of impurity scattering, as proposed by
Naveh and Laikhtman [Euro. Phys. Lett., 55, 545-551 (2001)]. Experimental
implications for the stability of proposed helical edge states will be
discussed.Comment: 5 pages, 4 figure
Scattering Theory for Quantum Hall Anyons in a Saddle Point Potential
We study the theory of scattering of two anyons in the presence of a
quadratic saddle-point potential and a perpendicular magnetic field. The
scattering problem decouples in the centre-of-mass and the relative
coordinates. The scattering theory for the relative coordinate encodes the
effects of anyon statistics in the two-particle scattering. This is fully
characterized by two energy-dependent scattering phase shifts. We develop a
method to solve this scattering problem numerically, using a generalized lowest
Landau level approximation.Comment: 5 pages. Published version, with clarified presentatio
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