60 research outputs found
A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra
We study finite loop models on a lattice wrapped around a cylinder. A section
of the cylinder has N sites. We use a family of link modules over the periodic
Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur,
and Graham and Lehrer. These are labeled by the numbers of sites N and of
defects d, and extend the standard modules of the original Temperley-Lieb
algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2}
(weight of contractible loops) and \alpha (weight of non-contractible loops),
this family also depends on a twist parameter v that keeps track of how the
defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends
on the anisotropy \nu and the spectral parameter \lambda that fixes the model.
(The thermodynamic limit of T_N is believed to describe a conformal field
theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).)
The family of periodic XXZ Hamiltonians is extended to depend on this new
parameter v and the relationship between this family and the loop models is
established. The Gram determinant for the natural bilinear form on these link
modules is shown to factorize in terms of an intertwiner i_N^d between these
link representations and the eigenspaces of S^z of the XXZ models. This map is
shown to be an isomorphism for generic values of u and v and the critical
curves in the plane of these parameters for which i_N^d fails to be an
isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop
models and XXZ Hamiltonians", 31 page
Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime
A recent theory has provided a possible explanation for the ``non-universal
scaling'' of the low-temperature conductance (and conductivity) peak-heights of
two-dimensional electron systems in the integer and fractional quantum Hall
regimes. This explanation is based on the hypothesis that samples which show
this behavior contain density inhomogeneities. Theory then relates the
non-universal conductance peak-heights to the ``number of alternating
percolation clusters'' of a continuum percolation model defined on the
spatially-varying local carrier density. We discuss the statistical properties
of the number of alternating percolation clusters for Corbino disc samples
characterized by random density fluctuations which have a correlation length
small compared to the sample size. This allows a determination of the
statistical properties of the low-temperature conductance peak-heights of such
samples. We focus on a range of filling fraction at the center of the plateau
transition for which the percolation model may be considered to be critical. We
appeal to conformal invariance of critical percolation and argue that the
properties of interest are directly related to the corresponding quantities
calculated numerically for bond-percolation on a cylinder. Our results allow a
lower bound to be placed on the non-universal conductance peak-heights, and we
compare these results with recent experimental measurements.Comment: 7 pages, 4 postscript figures included. Revtex with epsf.tex and
multicol.sty. The revised version contains some additional discussion of the
theory and slightly improved numerical result
Conformal Curves in Potts Model: Numerical Calculation
We calculated numerically the fractal dimension of the boundaries of the
Fortuin-Kasteleyn clusters of the -state Potts model for integer and
non-integer values of on the square lattice.
In addition we calculated with high accuracy the fractal dimension of the
boundary points of the same clusters on the square domain. Our calculation
confirms that this curves can be described by SLE.Comment: 11 Pages, 4 figure
Deformed strings in the Heisenberg model
We investigate solutions to the Bethe equations for the isotropic S = 1/2
Heisenberg chain involving complex, string-like rapidity configurations of
arbitrary length. Going beyond the traditional string hypothesis of undeformed
strings, we describe a general procedure to construct eigenstates including
strings with generic deformations, discuss general features of these solutions,
and provide a number of explicit examples including complete solutions for all
wavefunctions of short chains. We finally investigate some singular cases and
show from simple symmetry arguments that their contribution to zero-temperature
correlation functions vanishes.Comment: 34 pages, 13 figure
SLE local martingales in logarithmic representations
A space of local martingales of SLE type growth processes forms a
representation of Virasoro algebra, but apart from a few simplest cases not
much is known about this representation. The purpose of this article is to
exhibit examples of representations where L_0 is not diagonalizable - a
phenomenon characteristic of logarithmic conformal field theory. Furthermore,
we observe that the local martingales bear a close relation with the fusion
product of the boundary changing fields.
Our examples reproduce first of all many familiar logarithmic representations
at certain rational values of the central charge. In particular we discuss the
case of SLE(kappa=6) describing the exploration path in critical percolation,
and its relation with the question of operator content of the appropriate
conformal field theory of zero central charge. In this case one encounters
logarithms in a probabilistically transparent way, through conditioning on a
crossing event. But we also observe that some quite natural SLE variants
exhibit logarithmic behavior at all values of kappa, thus at all central
charges and not only at specific rational values.Comment: 40 pages, 7 figures. v3: completely rewritten, new title, new result
Anisotropy of magnetothermal conductivity in Sr2RuO4
The dependence of in-plane and interplane thermal conductivities of Sr2RuO4
on temperature, as well as magnetic field strength and orientation, is
reported. We found no notable anisotropy in the thermal conductivity for the
magnetic field rotation parallel to the conducting plane in the whole range of
experimental temperatures and fields, except in the vicinity of the upper
critical field Hc2, where the anisotropy of the Hc2 itself plays a dominant
role. This finding imposes strong constraints on the possible models of
superconductivity in Sr2RuO4 and supports the existence of a superconducting
gap with a line of nodes running orthogonal to the Fermi surface cylinder.Comment: published in Phys. Rev. Lett. 4pages, 4 eps figures, LaTe
Proposal for a CFT interpretation of Watts' differential equation for percolation
G. M. T. Watts derived that in two dimensional critical percolation the
crossing probability Pi_hv satisfies a fifth order differential equation which
includes another one of third order whose independent solutions describe the
physically relevant quantities 1, Pi_h, Pi_hv.
We will show that this differential equation can be derived from a level
three null vector condition of a rational c=-24 CFT and motivate how this
solution may be fitted into known properties of percolation.Comment: LaTeX, 20p, added references, corrected typos and additional content
Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
We find an explicit relation between the two known ways of generating an
infinite set of local conserved charges for the string sigma model on AdS_5 x
S^5: the Backlund and monodromy approaches. We start by constructing the
two-parameter family of Backlund transformations for the string with an
arbitrary world-sheet metric. We then show that only for a special value of one
of the parameters the solutions generated by this transformation are compatible
with the Virasoro constraints. By solving the Backlund equations in a
non-perturbative fashion, we finally show that the generating functional of the
Backlund conservation laws is equal to a certain sum of the quasi-momenta. The
positions of the quasi-momenta in the complex spectral plane are uniquely
determined by the real parameter of the Backlund transform.Comment: 25 pages, 1 figur
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