Condensed Matter Theory

Abstract:

Numerical results up to the 42nd order of replica-symmetry breaking (RSB) are used to predict the singular structure of the Sherrington-Kirkpatrick spin glass at T=0. We confirm predominant single parameter scaling and derive corrections for the T=0 order function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and a=infinity are shown to be two critical points for infinity-RSB, associated with two discrete spectra of Parisi block size ratios, attached to a continuous spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are obtained with unprecedented accuracy.

Abstract:

We develop a theoretical description of a Mach-Zehnder interferometer built from integer quantum Hall edge states, with an emphasis on how electron-electron interactions produce decoherence. We calculate the visibility of interference fringes and noise power, as a function of bias voltage and of temperature. Interactions are treated exactly, by using bosonization and considering edge states that are only weakly coupled via tunneling at the interferometer beam-splitters. In this weak-tunneling limit, we show that the bias-dependence of Aharonov-Bohm oscillations in source-drain conductance and noise power provides a direct measure of the one-electron correlation function for an isolated quantum Hall edge state. We find the asymptotic form of this correlation function for systems with either short-range interactions or unscreened Coulomb interactions, extracting a dephasing length $\ell_{\phi}$ that varies with temperature $T$ as $\ell_{\phi} \propto T^{-3}$ in the first case and as $\ell_{\phi} \propto T^{-1} \ln^2(T)$ in the second case.