Coherence and Partial Coherence in Interacting Electron Systems

We study coherence of electron transport through interacting quantum dots and discuss the relation of the coherent part to the flux-sensitive conductance for three different types of Aharonov-Bohm interferometers. Contributions to transport in first and second order in the intrinsic line width of the dot levels are addressed in detail. We predict an asymmetry of the interference signal around resonance peaks as a consequence of incoherence associated with spin-flip processes. Furthermore, we show by strict calculation that first-order contributions can be partially or even fully coherent. This contrasts with the sequential-tunneling picture which describes first-order transport as a sequence of incoherent tunneling processes

Restoration of Isotropy for Spin Models

Using real-space renormalisation techniques we analyse the Ising model on a Sierpi\'nski gasket with anisotropic microscopic couplings, and observe a restoration of isotropy on macroscopic scales. In particular, via use of a decimation procedure directly on the fractal lattice, we calculate explicitly the exponential anisotropy decay coefficients near the isotropic regime for both ferromagnetic and antiferromagnetic systems. The results suggest the universality of the phenomenon in lattice field theories on fractals.Comment: 10 pages, RevTeX, 4 postscript figures, to appear in Phys. Lett.

Intermediate fixed point in a Luttinger liquid with elastic and dissipative backscattering

In a recent work [Phys. Rev. Lett. {\bf 108}, 136401 (2012)] we have addressed the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. We have found that the physics associated with this model is qualitatively different from the elastic impurity setup analyzed by Kane and Fisher, and from the inelastic scattering scenario studied by Furusaki and Matveev, thus proposing a new paradigmatic picture of Luttinger liquid with an impurity. Here we present an extensive study of the renormalization group flows for this problem, the fixed point landscape, and scaling near those fixed points. Our analysis is non-perturbative in the elastic tunneling amplitudes, employing an instanton calculation in one or two of the available elastic tunneling channels. Our analysis accounts for non-trivial Klein factors, which represent anyonic or fermionic statistics. These Klein factors need to be taken into account due to the fact that higher order tunneling processes take place. In particular we find a stable fixed point, where an incoming current is split ${1 \over 2}$ - $1\over 2$ between a forward and a backward scattered beams. This intermediate fixed point, between complete backscattering and full forward scattering, is stable for the Luttinger parameter $g<1$.Comment: 21 pages, 12 figures, typos correcte

Control methods for improved Fisher information with quantum sensing

Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the relative phase is accumulated quadratically with time, and show that this can be produced by a variety of simple pulse sequences. Interestingly, this scaling has a limited duration, and we show that certain pulse sequences prolong the effect. The performance of these schemes is analyzed and we examine their relevance to state-of-the-art experiments. We analyze the $T^{3}$ scaling of the Fisher information which appears when multiple synchronized measurements are performed, and is the optimal scaling in the case of a finite coherence time

Dimer-monomer model on the Sierpinski gasket

We present the numbers of dimer-monomers on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are obtained.Comment: 30 pages, 10 figures, 10 table

Measurement and control of a Coulomb-blockaded parafermion box

Parafermionic zero modes are fractional topologically protected quasiparticles expected to arise in various platforms. We show that Coulomb charging effects define a parafermion box with unique access options via fractional edge states and/or quantum antidots. Basic protocols for the detection, manipulation, and control of parafermionic quantum states are formulated. With those tools, one may directly observe the dimension of the zero-mode Hilbert space, prove the degeneracy of this space, and perform on-demand digital operations satisfying a parafermionic algebra.Comment: 14 pages, 5 figures, supplemental material included as a PDF printou

Edge reconstruction in the ν=2/3\nu=2/3 fractional quantum Hall state

The edge structure of the $\nu=2/3$ fractional quantum Hall state has been studied for several decades but recent experiments, exhibiting upstream neutral mode(s), a plateau at a Hall conductance of $\frac{1}{3}( e^2/h)$ through a quantum point contact, and a crossover of the effective charge, from $e/3$ at high temperature to $2e/3$ at low temperature, could not be explained by a single theory. Here we develop such a theory, based on edge reconstruction due to a confining potential with finite slope, that admits an additional $\nu=1/3$ incompressible strip near the edge. Renormalization group analysis of the effective edge theory due to disorder and interactions explains the experimental observations.Comment: Published version, added references and clarification, minor editing to improve readability, added quantitative analysis of some experimental dat