arXiv subjects

Christoph Karrasch

Publications and source records attributed to Christoph Karrasch.

43 records · Page 3Linked to original sources

arXiv2017

Lower Bounding Diffusion Constant by the Curvature of Drude Weight

We establish a general connection between ballistic and diffusive transport in systems where the ballistic contribution in canonical ensemble vanishes. A lower bound on the Green-Kubo diffusion constant is derived in terms of the curvature of the ideal transport coefficient, the Drude weight, with respect to the filling parameter. As an application, we explicitly determine the lower bound on the high temperature diffusion constant in the anisotropic spin 1/2 Heisenberg chain for anisotropy parameters $Δ\geq 1$, thus settling the question whether the transport is sub-diffusive or not. Addi- tionally, the lower bound is shown to saturate the diffusion constant for a certain classical integrable model.

cond-mat.stat-mech↗

arXiv2017

Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no on finite region default of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.

cond-mat.dis-nn↗

arXiv2015

Expansion potentials for exact far-from-equilibrium spreading of particles and energy

The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), energy current in Lorentz-invariant theories or particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call ``expansion potentials'', expressed as integrals of equilibrium Drude weights. This relation between nonequilibrium quantities and linear response implies non-equilibrium Maxwell relations for the Drude weights. We verify our results via DMRG calculations for the XXZ chain.

cond-mat.str-el↗

arXiv2014

Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain

We investigate sudden quenches across the critical point in the transverse field Ising chain with a perturbing non-integrable next-nearest-neighbour interaction. Expressions for the return (Loschmidt) amplitude and associated rate function are derived to linear order in the next-nearest-neighbour coupling. In the thermodynamic limit these quantities exhibit non-analytic behaviour at a set of critical times, a phenomenon referred to as a dynamical quantum phase transition. We quantify the effect of the integrability breaking perturbation on the location and shape of these non-analyticities. Our results agree with those of earlier numerical studies and offer further support for the assertion that the dynamical quantum phase transitions exhibited by this model are a generic feature of its post-quench dynamics and is robust with respect to the inclusion of non-integrable perturbations.

cond-mat.stat-mech↗

arXiv2014

Time-evolving a matrix product state with long-ranged interactions

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting one-dimensional systems, such as Coulombic and dipolar systems, and quasi two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.

cond-mat.str-el↗

arXiv2012

Understanding the Josephson current through a Kondo-correlated quantum dot

We study the Josephson current 0-$π$ transition of a quantum dot tuned to the Kondo regime. The physics can be quantitatively captured by the numerically exact continuous time quantum Monte Carlo method applied to the single-impurity Anderson model with BCS superconducting leads. For a comparison to an experiment the tunnel couplings are determined by fitting the normal-state linear conductance. Excellent agreement for the dependence of the critical Josephson current on the level energy is achieved. For increased tunnel couplings the Kondo scale becomes comparable to the superconducting gap and the regime of the strongest competition between superconductivity and Kondo correlations is reached; we predict the gate voltage dependence of the critical current in this regime.

cond-mat.str-el↗

arXiv2007

A gentle introduction to the functional renormalization group: the Kondo effect in quantum dots

The functional renormalization group provides an efficient description of the interplay and competition of correlations on different energy scales in interacting Fermi systems. An exact hierarchy of flow equations yields the gradual evolution from a microscopic model Hamiltonian to the effective action as a function of a continuously decreasing energy cutoff. Practical implementations rely on suitable truncations of the hierarchy, which capture nonuniversal properties at higher energy scales in addition to the universal low-energy asymptotics. As a specific example we study transport properties through a single-level quantum dot coupled to Fermi liquid leads. In particular, we focus on the temperature T=0 gate voltage dependence of the linear conductance. A comparison with exact results shows that the functional renormalization group approach captures the broad resonance plateau as well as the emergence of the Kondo scale. It can be easily extended to more complex setups of quantum dots.

cond-mat.str-el↗