Wilson chains are not thermal reservoirs

Wilson chains, based on a logarithmic discretization of a continuous spectrum, are widely used to model an electronic (or bosonic) bath for Kondo spins and other quantum impurities within the numerical renormalization group method and other numerical approaches. In this short note we point out that Wilson chains can not serve as thermal reservoirs as their temperature changes by a number of order Delta E when a finite amount of energy Delta E is added. This proves that for a large class of non-equilibrium problems they cannot be used to predict the long-time behavior.Comment: 2 page

Mott transition of fermionic atoms in a three-dimensional optical trap

We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments.Comment: 4 pages and 5 figure

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.Comment: 4 pages, several minor modifications, title change

Lower bounds for the conductivities of correlated quantum systems

We show how one can obtain a lower bound for the electrical, spin or heat conductivity of correlated quantum systems described by Hamiltonians of the form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by conservation laws which lead to an infinite conductivity for g=0. The small perturbation g H1, however, renders the conductivity finite at finite temperatures. For example, H0 could be a continuum field theory, where momentum is conserved, or an integrable one-dimensional model while H1 might describe the effects of weak disorder. In the limit g to 0, we derive lower bounds for the relevant conductivities and show how they can be improved systematically using the memory matrix formalism. Furthermore, we discuss various applications and investigate under what conditions our lower bound may become exact.Comment: Title changed; 9 pages, 2 figure

Zero temperature optical conductivity of ultra-clean Fermi liquids and superconductors

We calculate the low-frequency optical conductivity sigma(w) of clean metals and superconductors at zero temperature neglecting the effects of impurities and phonons. In general, the frequency and temperature dependences of sigma have very little in common. For small Fermi surfaces in three dimensions (but not in 2D) we find for example that Re sigma(w>0)=const. for low w which corresponds to a scattering rate Gamma proportional to w^2 even in the absence of Umklapp scattering when there is no T^2 contribution to Gamma. In the main part of the paper we discuss in detail the optical conductivity of d-wave superconductors in 2D where Re sigma(w>0) \propto w^4 for the smallest frequencies and the Umklapp processes typically set in smoothly above a finite threshold w_0 smaller than twice the maximal gap Delta. In cases where the nodes are located at (pi/2, pi/2), such that direct Umklapp scattering among them is possible, one obtains Re sigma(w) \propto w^2.Comment: 7 pages, 3 figure

Kondo proximity effect: How does a metal penetrate into a Mott insulator?

We consider a heterostructure of a metal and a paramagnetic Mott insulator using an adaptation of dynamical mean field theory to describe inhomogeneous systems. The metal can penetrate into the insulator via the Kondo effect. We investigate the scaling properties of the metal-insulator interface close to the critical point of the Mott insulator. At criticality, the quasiparticle weight decays as 1/x^2 with distance x from the metal within our mean field theory. Our numerical results (using the numerical renormalization group as an impurity solver) show that the prefactor of this power law is extremely small.Comment: 4 pages, 3 figure

Anomalous bond stretching phonons as a probe of charge fluctuations in perovskites

Important information on momentum resolved low energy charge response can be extracted from anomalous properties of bond stretching in plane phonons observed in inelastic neutron and X-ray scattering in cuprates and some other perovskites. We discuss a semiphenomenological model based on coupling of phonons to a single charge mode. The phonon dispersion and linewidth allow to locate the energy of the charge excitation in the mid infrared part of the spectrum and to determine some of its characteristics. New experiments on oxygen isotope substitution could allow to achieve a more detailed description. Corresponding relations following from the model can be used for the interpretation of experiments and as test of the model.Comment: presented at the M2S-HTSC-VIII conference in Dresde

Current induced rotational torques in the skyrmion lattice phase of chiral magnets

In chiral magnets without inversion symmetry, the magnetic structure can form a lattice of magnetic whirl lines, a two-dimensional skyrmion lattice, stabilized by spin-orbit interactions in a small range of temperatures and magnetic fields. The twist of the magnetization within this phase gives rise to an efficient coupling of macroscopic magnetic domains to spin currents. We analyze the resulting spin-transfer effects, and, in particular, focus on the current induced rotation of the magnetic texture by an angle. Such a rotation can arise from macroscopic temperature gradients in the system as has recently been shown experimentally and theoretically. Here we investigate an alternative mechanism, where small distortions of the skyrmion lattice and the transfer of angular momentum to the underlying atomic lattice play the key role. We employ the Landau-Lifshitz-Gilbert equation and adapt the Thiele method to derive an effective equation of motion for the rotational degree of freedom. We discuss the dependence of the rotation angle on the orientation of the applied magnetic field and the distance to the phase transition.Comment: 11 pages, 6 figures; minor changes, published versio

Interplay of disorder and spin fluctuations in the resistivity near a quantum critical point

The resistivity in metals near an antiferromagnetic quantum critical point (QCP) is strongly affected by small amounts of disorder. In a quasi-classical treatment, we show that an interplay of strongly anisotropic scattering due to spin fluctuations and isotropic impurity scattering leads to a large regime where the resistivity varies as T^alpha, with an anomalous exponent, alpha, 1 <= alpha <= 1.5, depending on the amount of disorder. I argue that this mechanism explains in some detail the anomalous temperature dependence of the resistivity observed in CePd_2Si_2, CeNi_2Ge_2 and CeIn_3 near the QCP.Comment: 4 pages, 4 eps figures, published version, only small change