Claudio Chamon

Two-dimensional conformal field theory for disordered systems at criticality

Using a Kac-Moody current algebra with U(1/1) × U(1/1) graded symmetry, we describe a class of (possibly disordered) critical points in two spatial dimensions. The critical points are labelled by the triplets (l, m, kj), where l is an odd integer, m is an integer, and kj is real. For most such critical points, we show that there are infinite hierarchies of relevant operators with negative scaling dimensions. To interpret this result, we show that the line of critical points (1, 1, kj > 0) is realized by a field theory of massless Dirac fermions in the presence of U(N) vector gauge-like static impurities. Along the disordered critical line (1, 1, kj > 0) we find an infinite hierarchy of relevant operators with negative scaling dimensions {δq∥q ϵ N}, which are related to the disorder average over the qth moment of the single-particle Green function. Those relevant operators can be induced by non-Gaussian moments of the probability distribution of a mass-like static disorder.

Localization in Two Dimensions, Gaussian Field Theories, and Multifractality.

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.

Irrational versus rational charge and statistics in two-dimensional quantum systems.

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-binding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge rerationalizes to the value 1/2 and the exchange statistics to that of quartons (half-semions).

Instability of the disordered critical points of Dirac fermions.

Recently, in an attempt to study disordered criticality in Quantum Hall systems and

The quantum three-coloring dimer model and its line of critical points that is interrupted by quantum glassiness

d

Wire deconstructionism and classification of topological phases

-wave superconductivity, it was found that two dimensional random Dirac fermion systems contain a line of critical points which is connected to the pure system. We use bosonization and current algebra to study properties of the critical line and calculate the exact scaling dimensions of all local operators. We find that the critical line contains an infinite number of relevant operators with negative scaling dimensions.