Signatures of integrability in charge and thermal transport in 1D quantum systems

Integrable and non-integrable systems have very different transport properties. In this work, we highlight these differences for specific one dimensional models of interacting lattice fermions using numerical exact diagonalization. We calculate the finite temperature adiabatic stiffness (or Drude weight) and isothermal stiffness (or ``Meissner'' stiffness) in electrical and thermal transport and also compute the complete momentum and frequency dependent dynamical conductivities $\sigma(q,\omega)$ and $\kappa(q,\omega)$. The Meissner stiffness goes to zero rapidly with system size for both integrable and non-integrable systems. The Drude weight shows signs of diffusion in the non-integrable system and ballistic behavior in the integrable system. The dynamical conductivities are also consistent with ballistic and diffusive behavior in the integrable and non-integrable systems respectively.Comment: 4 pages, 4 figure

Magnon Heat Transport in doped La2CuO4\rm La_2CuO_4

We present results of the thermal conductivity of $\rm La_2CuO_4$ and $\rm La_{1.8}Eu_{0.2}CuO_4$ single-crystals which represent model systems for the two-dimensional spin-1/2 Heisenberg antiferromagnet on a square lattice. We find large anisotropies of the thermal conductivity, which are explained in terms of two-dimensional heat conduction by magnons within the CuO$_2$ planes. Non-magnetic Zn substituted for Cu gradually suppresses this magnon thermal conductivity $\kappa_{\mathrm{mag}}$. A semiclassical analysis of $\kappa_{\mathrm{mag}}$ is shown to yield a magnon mean free path which scales linearly with the reciprocal concentration of Zn-ions.Comment: 4 pages, 3 figure

Magnetic heat conductivity in CaCu2O3\rm\bf CaCu_2O_3: linear temperature dependence

We present experimental results for the thermal conductivity $\kappa$ of the pseudo 2-leg ladder material $\rm CaCu_2O_3$. The strong buckling of the ladder rungs renders this material a good approximation to a $S=1/2$ Heisenberg-chain. Despite a strong suppression of the thermal conductivity of this material in all crystal directions due to inherent disorder, we find a dominant magnetic contribution $\kappa_\mathrm{mag}$ along the chain direction. $\kappa_\mathrm{mag}$ is \textit{linear} in temperature, resembling the low-temperature limit of the thermal Drude weight $D_\mathrm{th}$ of the $S=1/2$ Heisenberg chain. The comparison of $\kappa_\mathrm{mag}$ and $D_\mathrm{th}$ yields a magnetic mean free path of $l_\mathrm{mag}\approx 22 \pm 5$ \AA, in good agreement with magnetic measurements.Comment: appears in PR

Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Anomalous magnetothermal effects are discussed in the spin-1/2 Heisenberg chain. The energy current is related to one of the non-trivial conserved quantities underlying integrability and therefore both the diagonal and off diagonal dynamical correlations of spin and energy current diverge. The energy-energy and spin-energy current correlations at finite temperatures are exactly calculated by a lattice path integral formulation. The low-temperature behavior of the thermomagnetic (magnetic Seebeck) coefficient is also discussed. Due to effects of strong correlations, we observe the magnetic Seebeck coefficient changes sign at certain interaction strengths and magnetic fields.Comment: 4 pages, references added, typos corrected, Conference proceedings of SPQS 2004, Sendai, Japa

Transport through quantum dots: A combined DMRG and cluster-embedding study

The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation (ECA), rely on the numerical solution of clusters of finite size. For the interpretation of numerical results, it is therefore crucial to understand finite-size effects in detail. In this work, we present a careful finite-size analysis for the examples of one quantum dot, as well as three serially connected quantum dots. Depending on odd-even effects, physically quite different results may emerge from clusters that do not differ much in their size. We provide a solution to a recent controversy over results obtained with ECA for three quantum dots. In particular, using the optimum clusters discussed in this paper, the parameter range in which ECA can reliably be applied is increased, as we show for the case of three quantum dots. As a practical procedure, we propose that a comparison of results for static quantities against those of quasi-exact methods, such as the ground-state density matrix renormalization group (DMRG) method or exact diagonalization, serves to identify the optimum cluster type. In the examples studied here, we find that to observe signatures of the Kondo effect in finite systems, the best clusters involving dots and leads must have a total z-component of the spin equal to zero.Comment: 16 pages, 14 figures, revised version to appear in Eur. Phys. J. B, additional reference

Exact results for nonlinear ac-transport through a resonant level model

We obtain exact results for the transport through a resonant level model (noninteracting Anderson impurity model) for rectangular voltage bias as a function of time. We study both the transient behavior after switching on the tunneling at time t = 0 and the ensuing steady state behavior. Explicit expressions are obtained for the ac-current in the linear response regime and beyond for large voltage bias. Among other effects, we observe current ringing and PAT (photon assisted tunneling) oscillations.Comment: 7 page

A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.Comment: 17 pages, 13 figure

Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain

Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.Comment: 8 page