Lightcone renormalization and quantum quenches in one-dimensional Hubbard models

The Lieb-Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm based on this light cone structure to study the time evolution of prepared initial states in the thermodynamic limit in one-dimensional quantum systems. The algorithm does not require translational invariance and allows for an easy implementation of local conservation laws. We use the algorithm to investigate the relaxation dynamics of double occupancies in fermionic Hubbard models as well as a possible thermalization. For the integrable Hubbard model we find a pure power-law decay of the number of doubly occupied sites towards the value in the long-time limit while the decay becomes exponential when adding a nearest neighbor interaction. In accordance with the eigenstate thermalization hypothesis, the long-time limit is reasonably well described by a thermal average. We point out though that such a description naturally requires the use of negative temperatures. Finally, we study a doublon impurity in a N\'eel background and find that the excess charge and spin spread at different velocities, providing an example of spin-charge separation in a highly excited state.Comment: published versio

Kondo physics in transport through a quantum dot with Luttinger liquid leads

We study the gate voltage dependence of the linear conductance through a quantum dot coupled to one-dimensional leads. For interacting dot electrons but noninteracting leads Kondo physics implies broad plateau-like resonances. In the opposite case Luttinger liquid behavior leads to sharp resonances. In the presence of Kondo as well as Luttinger liquid physics and for experimentally relevant parameters, we find a line shape that resembles the one of the Kondo case.Comment: 4+ pages, 4 figures include

High-Velocity Estimates and Inverse Scattering for Quantum N-Body Systems with Stark Effect

In an N-body quantum system with a constant electric field, by inverse scattering, we uniquely reconstruct pair potentials, belonging to the optimal class of short-range potentials and long-range potentials, from the high-velocity limit of the Dollard scattering operator. We give a reconstruction formula with an error term.Comment: In this published version we have added remarks and we have edited the pape

On the contribution of nearly-critical spin and charge collective modes to the Raman spectra of high-Tc cuprates

We discuss how Raman spectra are affected by nearly-critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We show that specific fingerprints of nearly-critical collective modes can indeed be observed in Raman spectra and that the selectivity of Raman spectroscopy in momentum space may also be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-Tc superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover spin modes should be more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuate with high frequency.Comment: 5 pages, 3 figure

Is local scale invariance a generic property of ageing phenomena ?

In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J. Phys. A 37, 10479] it is shown that the critical autoresponse function of the 1+1-dimensional contact process is not in agreement with the predictions of local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques

Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity

We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1/2 fermions. The underlying approximations are devised for weak interactions and arbitrary impurity strengths, and have been checked by comparing with density-matrix renormalization-group data. We present results for the density of states, the density profile and the linear conductance. Two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.Comment: 36 pages, 13 figures, revised version as publishe

Strain sensing with sub-micron sized Al-AlOx-Al tunnel junctions

We demonstrate a local strain sensing method for nanostructures based on metallic Al tunnel junctions with AlOx barriers. The junctions were fabricated on top of a thin silicon nitride membrane, which was actuated with an AFM tip attached to a stiff cantilever. A large relative change in the tunneling resistance in response to the applied strain (gauge factor) was observed, up to a value 37. This facilitates local static strain variation measurements down to ~10^{-7}.Comment: 4 pages, 3 figure