41 research outputs found
Renormalization group for network models of Quantum Hall transitions
We analyze in detail the renormalization group flows which follow from the
recently proposed all orders beta functions for the Chalker-Coddington network
model. The flows in the physical regime reach a true singularity after a finite
scale transformation. Other flows are regular and we identify the asymptotic
directions. One direction is in the same universality class as the disordered
XY model.
The all orders beta function is computed for the network model of the spin
Quantum Hall transition and the flows are shown to have similar properties. It
is argued that fixed points of general current-current interactions in 2d
should correspond to solutions of the Virasoro master equation. Based on this
we identify two coset conformal field theories osp(2N|2N)_1 /u(1)_0 and
osp(4N|4N)_1/su(2)_0 as possible fixed points and study the resulting
multifractal properties. We also obtain a scaling relation between the typical
amplitude exponent alpha_0 and the typical point contact conductance exponent
X_t which is expected to hold when the density of states is constant.Comment: 35 pages, 5 color figures, v2: references adde
Affine Lie Algebra Symmetry of Sine-Gordon Theory at Reflectionless Points
The quantum affine symmetry of the sine-Gordon theory at q^2 = 1, which
occurs at the reflectionless points, is studied. Conserved currents that
correspond to the closure of simple root generators are considered, and shown
to be local. We argue that they satisfy the affine sl(2) algebra. Examples of
these currents are explicitly constructed.Comment: 8 pages, plaintex, uses harvma
Strong-weak coupling duality in anisotropic current interactions
The recently proposed all orders beta function is further investigated. By
using a strong-weak coupling duality of the beta function, and some added
topology of the space of couplings we are able to extend the flows to
arbitrarily large or small scales. Using a non-trivial RG invariant we are able
to identify sine-Gordon, sinh-Gordon and Kosterlitz-Thouless phases. We also
find an additional phase with cyclic or roaming RG trajectories.Comment: 10 pages, 1 color figure v2: additional check with both UV and IR
fixed points include