No abstract

We have recently calculated exact non-equilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact I(V ) characteristic and conductance out of equilibrium as a function of driving voltage V and temperature T . These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and V /T . The differential-conductance curve as a function of the interaction strength broadens significantly as V /T is increased, and develops a pronounced maximum at a (universal) critical value (eV /k B T ) = 7.18868 . . .. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling. † A.P. Sloan Fellow * Packard Fellow 3/95

The conductance for tunneling through a point contact between two ν = 1/3 quantum Hall edges is described by a universal scaling function, which has recently been measured experimentally. We compute this universal function exactly, by using the thermodynamic Bethe ansatz and a Boltzmann equation.

We study two-dimensional nonlinear sigma models in which the target spaces are the coset supermanifolds U(n + m|n)/[U(1)×U(n + m − 1|n)] ∼ = CP n+m−1|n (projective superspaces) and OSp(2n + m|2n)/OSp(2n + m − 1|2n) ∼ = S 2n+m−1|2n (superspheres), n, m integers, −2 ≤ m ≤ 2; these quantum field theories live in Hilbert spaces with indefinite inner products. These theories possess non-trivial conformally-invariant renormalization-group fixed points, or in some cases, lines of fixed points. Some of the conformal fixed-point theories can also be obtained within LandauGinzburg theories. We obtain the complete spectra (with multiplicities) of exact conformal weights of states (or corresponding local operators) in the isolated fixed-point conformal field theories, and at one special point on each of the lines of fixed points. Although the conformal weights are rational, the conformal field theories are not, and (with one exception) do not contain the affine versions of their superalgebras in their chiral algebras. The method involves lattice models that represent the strong-coupling region, which can be mapped to loop models, and then to a Coulomb gas with modified boundary conditions. The results apply to percolation, dilute and dense polymers, and other statistical mechanics models, and also to the spin quantum Hall transition in noninteracting fermions with quenched disorder.