arXiv subjects

D. M. Kennes

Publications and source records attributed to D. M. Kennes.

48 records · Page 3Linked to original sources

arXiv2014

Universal quench dynamics of interacting quantum impurity systems

The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale $T_K$ (Kondo temperature) that breaks scale invariance. For the non-interacting resonant level model, the non-equilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitely [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable $T_K t$. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two non-interacting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field theory predictions for the universal scaling as well as for the large time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models.

cond-mat.str-el↗

arXiv2014

Spectral properties of one-dimensional Fermi systems after an interaction quench

We show that the single-particle spectral properties of gapless one-dimensional Fermi systems in the Luttinger liquid state reached at intermediate times after an abrupt quench of the two-particle interaction are highly indicative of the unusual nonequilibrium nature of this state. The line shapes of the momentum integrated and resolved spectral functions strongly differ from their ground state as well as finite temperature equilibrium counterparts. Using an energy resolution improved version of radio-frequency spectroscopy of quasi one-dimensional cold Fermi gases it should be possible to experimentally identify this nonequilibrium state by its pronounced spectral signatures.

cond-mat.str-el↗

arXiv2014

Renormalization group flows in one-dimensional lattice models: impurity scaling, umklapp scattering and the orthogonality catastrophe

We show that to understand the orthogonality catastrophe in the half-filled lattice model of spinless fermions with repulsive nearest neighbor interaction and a local impurity in its Luttinger liquid phase one has to take into account (i) the impurity scaling, (ii) unusual finite size $L$ corrections of the form $\ln(L)/L$, as well as (iii) the renormalization group flow of the umklapp scattering. The latter defines a length scale $L_u$ which becomes exceedingly large the closer the system is to its transition into the charge-density wave phase. Beyond this transition umklapp scattering is relevant in the renormalization group sense. Field theory can only be employed for length scales larger than $L_u$. For small to intermediate two-particle interactions, for which the regime $L > L_u$ can be accessed, and taking into account the finite size corrections resulting from (i) and (ii) we provide strong evidence that the impurity backscattering contribution to the orthogonality exponent is asymptotically given by $1/16$. While further increasing the two-particle interaction leads to a faster renormalization group flow of the impurity towards the cut chain fixed point, the increased bare amplitude of the umklapp scattering renders it virtually impossible to confirm the expected asymptotic value of $1/16$ given the accessible system sizes. We employ the density matrix renormalization group.

cond-mat.str-el↗

arXiv2014

Dynamical regimes of dissipative quantum systems

We reveal several distinct regimes of the relaxation dynamics of a small quantum system coupled to an environment within the plane of the dissipation strength and the reservoir temperature. This is achieved by discriminating between coherent dynamics with damped oscillatory behavior on all time scales, partially coherent behavior being nonmonotonic at intermediate times but monotonic at large ones, and purely monotonic incoherent decay. Surprisingly, elevated temperature can render the system `more coherent' by inducing a transition from the partially coherent to the coherent regime. This provides a refined view on the relaxation dynamics of open quantum systems.

quant-ph↗

arXiv2014

Extending the range of real time density matrix renormalization group simulations

We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications almost effortlessly within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schroedinger and Heisenberg time evolutions of arbitrary pure states |psi> and operators A in the evaluation of _psi(t)= . This includes quantum quenches. The generalization (non-)thermal mixed state dynamics _rho(t)=Tr[rho A(t)] induced by an initial density matrix rho is straightforward. In the context of equilibrium (ground state or finite temperature T>0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T>0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.

cond-mat.str-el↗

arXiv2013

Luttinger liquid properties of the steady state after a quantum quench

We study the dynamics resulting out of an abrupt change of the two-particle interaction in two models of closed one-dimensional Fermi systems: (a) the field theoretical Tomonaga-Luttinger model and (b) a microscopic lattice model. Using a nonperturbative approach which is controlled for small two-particle interactions we are able to reach large times allowing us to access the properties of the steady state of the lattice model. Comparing those to the exact solution of the full dynamics in the Tomonaga-Luttinger model we provide evidence for universal Luttinger liquid behavior.

cond-mat.str-el↗

arXiv2013

Functional renormalization group study of the Anderson--Holstein model

We present a comprehensive study of the spectral and transport properties in the Anderson--Holstein model both in and out of equilibrium using the functional renormalization group (FRG). We show how the previously established machinery of Matsubara and Keldysh FRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron--phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the non-linear differential conductance through the Anderson--Holstein quantum dot and find clear signatures of the presence of the phonon mode.

cond-mat.str-el↗

arXiv2013

Efficiency and power of a thermoelectric quantum dot device

We study linear response and nonequilibrium steady-state thermoelectric transport through a single-level quantum dot tunnel coupled to two reservoirs held at different temperatures as well as chemical potentials. A fermion occupying the dot interacts with those in the reservoirs by a short-ranged two-particle interaction. For parameters for which particles flow against a bias voltage from the hot to the cold reservoir this setup acts as an energy-conversion device with which electrical energy is gained out of waste heat. We investigate how correlations affect its efficiency and output power. In linear response the changes in the thermoelectric properties can be traced back to the interaction induced renormalization of the resonance line shape. In particular, small to intermediate repulsive interactions reduce the maximum efficiency. In nonequilibrium the situation is more complex and we identify a parameter regime in which for a fixed lower bound of the output power the efficiency increases.

cond-mat.str-el↗

arXiv2013

The interacting resonant level model in nonequilibrium: finite temperature effects

We study the steady-state properties as well as the relaxation dynamics of the nonequilibrium interacting resonant level model at finite temperatures. It constitutes the prototype model of a correlated charge fluctuating quantum dot. The two reservoirs are held at different chemical potentials---the difference being the bias voltage---and different temperatures; we discuss the transport through as well as the occupancy of the single level dot. First, we show analytically that in the steady state the reservoir temperatures in competition with the other energy scales act as infrared cutoffs. This is rather intuitive but, depending on the parameter regime under consideration, leads to a surprisingly rich variety of power laws in the current as a function of the temperatures and the bias voltage with different interaction dependent exponents. Next we clarify how finite reservoir temperatures affect the dynamics. They allow to tune the interplay of the two frequencies characterizing the oscillatory part of the time evolution of the model at zero temperature. For the exponentially decaying part we disentangle the contributions of the level-lead hybridization and the temperatures to the decay rates. We identify a coherent-to-incoherent transition in the long time dynamics as the temperature is raised. It occurs at an interaction dependent critical temperature. Finally, taking different temperatures in the reservoirs we discuss the relaxation dynamics of a temperature gradient driven current.

cond-mat.str-el↗

arXiv2013

Oscillatory dynamics and non-markovian memory in dissipative quantum systems

The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (1) the oscillatory dynamics close to a coherent-to-incoherent transition is surprisingly different from the one of the classical damped harmonic oscillator and that (2) non-markovian memory plays a prominent role in the time evolution after a quantum quench.

cond-mat.str-el↗

arXiv2011

A renormalization group approach to time dependent transport through correlated quantum dots

We introduce a real time version of the functional renormalization group which allows to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a nonequilibrium initial state into a (potentially) steady state driven by a bias voltage and (ii) the dynamics governed by an explicitly time-dependent Hamiltonian. All time regimes from transient to asymptotic can be tackled; the only approximation is the consistent truncation of the flow equations at a given order. As an application we investigate the relaxation dynamics of the interacting resonant level model which describes a fermionic quantum dot dominated by charge fluctuations. Moreover, we study decoherence and relaxation phenomena within the ohmic spin-boson model by mapping the latter to the interacting resonant level model.

cond-mat.str-el↗

arXiv2010

Relaxation dynamics of an exactly solvable electron-phonon model

We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a stationary density matrix. Two initial nonequilibrium situations are considered. A sudden quench of the electron-phonon coupling, starting from the noninteracting canonical equilibrium at temperature T in the electron as well as in the phonon subsystems, leads to a rather simple dynamics. A richer time evolution emerges if the initial state is taken as the product of the phonon vacuum and the filled Fermi sea supplemented by a highly excited additional electron. Our model has a natural set of constants of motion, with as many elements as degrees of freedom. In accordance with earlier studies of such type of models we find that expectation values which become stationary can be described by the density matrix of a generalized Gibbs ensemble which differs from that of a canonical ensemble. For the model at hand it appears to be evident that the eigenmode occupancy operators should be used in the construction of the stationary density matrix.

cond-mat.str-el↗