16,081 research outputs found
Edge states and conformal boundary conditions in super spin chains and super sigma models
The sigma models on projective superspaces CP^{N+M-1|N} with topological
angle theta=pi mod 2pi flow to non-unitary, logarithmic conformal field
theories in the low-energy limit. In this paper, we determine the exact
spectrum of these theories for all open boundary conditions preserving the full
global symmetry of the model, generalizing recent work on the particular case
M=0 [C. Candu et al, JHEP02(2010)015]. In the sigma model setting, these
boundary conditions are associated with complex line bundles, and are labelled
by an integer, related with the exact value of theta. Our approach relies on a
spin chain regularization, where the boundary conditions now correspond to the
introduction of additional edge states. The exact values of the exponents then
follow from a lengthy algebraic analysis, a reformulation of the spin chain in
terms of crossing and non-crossing loops (represented as a certain subalgebra
of the Brauer algebra), and earlier results on the so-called one- and
two-boundary Temperley Lieb algebras (also known as blob algebras). A
remarkable result is that the exponents, in general, turn out to be irrational.
The case M=1 has direct applications to the spin quantum Hall effect, which
will be discussed in a sequel.Comment: 50 pages, 18 figure
Freezing transitions and the density of states of 2D random Dirac Hamiltonians
Using an exact mapping to disordered Coulomb gases, we introduce a novel
method to study two dimensional Dirac fermions with quenched disorder in two
dimensions which allows to treat non perturbative freezing phenomena. For
purely random gauge disorder it is known that the exact zero energy eigenstate
exhibits a freezing-like transition at a threshold value of disorder
. Here we compute the dynamical exponent which
characterizes the critical behaviour of the density of states around zero
energy, and find that it also exhibits a phase transition. Specifically, we
find that (and ) with for and
for . For a finite system size we find large
sample to sample fluctuations with a typical .
Adding a scalar random potential of small variance , as in the
corresponding quantum Hall system, yields a finite noncritical whose scaling exponent exhibits two transitions, one
at and the other at . These transitions are shown
to be related to the one of a directed polymer on a Cayley tree with random
signs (or complex) Boltzmann weights. Some observations are made for the strong
disorder regime relevant to describe transport in the quantum Hall system
Phase Structure of d=2+1 Compact Lattice Gauge Theories and the Transition from Mott Insulator to Fractionalized Insulator
Large-scale Monte Carlo simulations are employed to study phase transitions
in the three-dimensional compact abelian Higgs model in adjoint representations
of the matter field, labelled by an integer q, for q=2,3,4,5. We also study
various limiting cases of the model, such as the lattice gauge theory,
dual to the spin model, and the 3DXY spin model which is dual to the
lattice gauge theory in the limit . We have computed the
first, second, and third moments of the action to locate the phase transition
of the model in the parameter space , where is the
coupling constant of the matter term, and is the coupling constant of
the gauge term. We have found that for q=3, the three-dimensional compact
abelian Higgs model has a phase-transition line which
is first order for below a finite {\it tricritical} value
, and second order above. We have found that the
first order phase transition persists for finite and
joins the second order phase transition at a tricritical point
. For
all other integer we have considered, the entire phase transition
line is critical.Comment: 17 pages, 12 figures (new Fig. 2), new Section IVB, updated
references, submitted to Physical Review
Nishimori point in the 2D +/- J random-bond Ising model
We study the universality class of the Nishimori point in the 2D +/- J
random-bond Ising model by means of the numerical transfer-matrix method. Using
the domain-wall free-energy, we locate the position of the fixed point along
the Nishimori line at the critical concentration value p_c = 0.1094 +/- 0.0002
and estimate nu = 1.33 +/- 0.03. Then, we obtain the exponents for the moments
of the spin-spin correlation functions as well as the value for the central
charge c = 0.464 +/- 0.004. The main qualitative result is the fact that
percolation is now excluded as a candidate for describing the universality
class of this fixed point.Comment: 4 pages REVTeX, 3 PostScript figures; final version to appear in
Phys. Rev. Lett.; several small changes and extended explanation
Point-Contact Conductances at the Quantum Hall Transition
On the basis of the Chalker-Coddington network model, a numerical and
analytical study is made of the statistics of point-contact conductances for
systems in the integer quantum Hall regime. In the Hall plateau region the
point-contact conductances reflect strong localization of the electrons, while
near the plateau transition they exhibit strong mesoscopic fluctuations. By
mapping the network model on a supersymmetric vertex model with GL(2|2)
symmetry, and postulating a two-point correlator in keeping with the rules of
conformal field theory, we derive an explicit expression for the distribution
of conductances at criticality. There is only one free parameter, the power law
exponent of the typical conductance. Its value is computed numerically to be
X_t = 0.640 +/- 0.009. The predicted conductance distribution agrees well with
the numerical data. For large distances between the two contacts, the
distribution can be described by a multifractal spectrum solely determined by
X_t. Our results demonstrate that multifractality can show up in appropriate
transport experiments.Comment: 18 pages, 15 figures included, revised versio
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