A commercially available calorimeter has been used to investigate the specific heat of a high-quality \kn\ single crystal. The addenda heat capacity of the calorimeter is determined in the temperature range $0.02 \, \mathrm{K} \leq T \leq 0.54 \, \mathrm{K}$. The data of the \kn\ crystal imply the presence of a large $T^2$ contribution to the specific heat which gives evidence of $d$-wave order parameter symmetry in the superconducting state. To improve the measurements, a novel design for a calorimeter with a paramagnetic temperature sensor is presented. It promises a temperature resolution of $\Delta T \approx 0.1 \, \mathrm{\mu K}$ and an addenda heat capacity less than $200 \, \mathrm{pJ/K}$ at $ T < 100 \, \mathrm{mK}$.

A. Reifenberger M. Hempel P. Vogt S. Aswartham M. Abdel-Hafiez V. Grinenko S. Wurmehl S. -L. Drechsler A. Fleischmann C. Enss R. Klingeler

We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector $k_F^{-1}$, we find that the bare transverse spin diffusivity reaches a minimum of $1.7(6)\hbar/m$, where $m$ is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. At unitarity, the contact rises to $0.28(3) k_F^2$ per particle, measuring the breaking of scaling symmetry. Our observations support the conjecture that in systems with strong scattering, the local relaxation rate is bounded from above by $k_B T/\hbar$.

C. Luciuk S. Smale F. Böttcher H. Sharum B. A. Olsen S. Trotzky T. Enss J. H. Thywissen

We improve the recently developed functional renormalization group (fRG) for impurities and boundaries in Luttinger liquids by including renormalization of the two-particle interaction, in addition to renormalization of the impurity potential. Explicit flow-equations are derived for spinless lattice fermions with nearest neighbor interaction at zero temperature, and a fast algorithm for solving these equations for very large systems is presented. We compute spectral properties of single-particle excitations, and the oscillations in the density profile induced by impurities or boundaries for chains with up to 1000000 lattice sites. The expected asymptotic power-laws at low energy or long distance are fully captured by the fRG. Results on the relevant energy scales and crossover phenomena at intermediate scales are also obtained. A comparison with numerical density matrix renormalization results for systems with up to 1000 sites shows that the fRG with the inclusion of vertex renormalization is remarkably accurate even for intermediate interaction strengths.

S. Andergassen T. Enss V. Meden W. Metzner U. Schollwoeck K. Schoenhammer

We study transport through a one-dimensional quantum wire of correlated fermions connected to semi-infinite leads. The wire contains either a single impurity or two barriers, the latter allowing for resonant tunneling. In the leads the fermions are assumed to be non-interacting. The wire is described by a microscopic lattice model. Using the functional renormalization group we calculate the linear conductance for wires of mesoscopic length and for all relevant temperature scales. For a single impurity, either strong or weak, we find power-law behavior as a function of temperature. In addition, we can describe the complete crossover from the weak- to the strong-impurity limit. For two barriers, depending on the parameters of the enclosed quantum dot, we find temperature regimes in which the conductance follows power-laws with "universal" exponents as well as non-universal behavior. Our approach leads to a comprehensive picture of resonant tunneling. We compare our results with those of alternative approaches.

T. Enss V. Meden S. Andergassen X. Barnabe-Theriault W. Metzner K. Schoenhammer

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.

S. Andergassen T. Enss V. Meden W. Metzner U. Schollwoeck K. Schoenhammer

We investigate the effect of local Coulomb correlations on electronic transport through a variety of coupled quantum dot systems connected to Fermi liquid leads. We use a newly developed functional renormalization group scheme to compute the gate voltage dependence of the linear conductance, the transmission phase, and the dot occupancies. A detailed derivation of the flow equations for the dot level positions, the inter-dot hybridizations, and the effective interaction is presented. For specific setups and parameter sets we compare the results to existing accurate numerical renormalization group data. This shows that our approach covers the essential physics and is quantitatively correct up to fairly large Coulomb interactions while being much faster, very flexible, and simple to implement. We then demonstrate the power of our method to uncover interesting new physics. In several dots coupled in series the combined effect of correlations and asymmetry leads to a vanishing of transmission resonances. In contrast, for a parallel double-dot we find parameter regimes in which the two-particle interaction generates additional resonances.

C. Karrasch T. Enss V. Meden

We analyse phase averaging in one-dimensional interacting mesoscopic systems with several barriers and show that for incommensurate positions an independent average over several phases can be induced by finite temperature. For three strong barriers with conductances G_i and mutual distances larger than the thermal length, we obtain G ~ sqrt{G_1 G_2 G_3} for the total conductance G. For an interacting wire, this implies power laws in G(T) with novel exponents, which we propose as an experimental fingerprint to distinguish temperature induced phase averaging from dephasing.

Severin G. Jakobs Volker Meden Herbert Schoeller Tilman Enss

Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling, J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber dynamics quenched to the critical point. At variance with the results of Henkel et al., we detect discrepancies between the actual scaling behavior of the response function and the prediction of Local Scale Invariance. Such differences are clearly visible in the impulse autoresponse function, whereas they are drastically reduced in integrated response functions. Accordingly, the scaling form predicted on the basis of Local Scale Invariance simply provides an accurate fitting form for some quantities but cannot be considered to be exact.

Federico Corberi Andrea Gambassi Eugenio Lippiello Marco Zannetti

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.

S. Caprara C. Di Castro T. Enss M. Grilli

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

M. Grilli S. Caprara C. Di Castro T. Enss R. Hackl B. Muschler W. Prestel