arXiv subjects

S. Kehrein

Publications and source records attributed to S. Kehrein.

At least 19 recordsLinked to original sources

arXiv2014

Dissipation-induced first-order decoherence phase transition in a non-interacting fermionic system

We consider a dissipative tight-binding chain. The dissipation manifests as tunneling into/out of the chain from/to a memoryless environment. The evolution of the system is described by the Lindblad equation. Already infinitesimally small dissipation along the chain induces a quantum phase transition (QPT). This is a decoherence QPT: the reduced density matrix of a subsystem (far from the ends of the chain) can be represented as the tensor product of single-site density matrices. We analyze the QPT in the thermodynamic limit by looking at the entropy and the response function in the bulk. We also explore the properties of the boundaries of the chain close to the transition point and observe that the boundaries behave as if they undergo a second-order phase transition with power-law divergence of the correlation functions and response function. Disorder is known to localize one-dimensional systems, but the coupling to the memoryless environment pushes the system back into the delocalized state even in the presence of disorder.

cond-mat.mes-hall↗

arXiv2014

Power-law approach to steady state in open lattices of non-interacting electrons

We address the question of how a non-equilibrium steady state (NESS) is reached in the Linbdladian dynamics of an open quantum system. We develop an expansion of the density matrix in terms of the NESS-excitations, each of which has its own (exponential) decay rate. However, when the decay rates tend to zero for many NESS-excitations (the spectral gap of the Liouvillian is closed in the thermodynamic limit), the long-time dynamics of the system can exhibit a power-law behaviour. This relaxation to NESS expectation values is determined by the density of states close to zero spectral gap and the value of the operator in these states. We illustrate this main idea on the example of the lattice of non-interacting fermions coupled to Markovian leads at infinite bias voltage. The current comes towards its NESS value starting from a typical initial state as $τ^{-3/2}$. This behaviour is universal and independent of the space dimension.

cond-mat.mes-hall↗

arXiv2014

Quench Dynamics in a Model with Tuneable Integrability Breaking

We consider quantum quenches in an integrable quantum chain with tuneable-integrability-breaking interactions. In the case where these interactions are weak, we demonstrate that at intermediate times after the quench local observables relax to a prethermalized regime, which can be described by a density matrix that can be viewed as a deformation of a generalized Gibbs ensemble. We present explicit expressions for the approximately conserved charges characterizing this ensemble. We do not find evidence for a crossover from the prethermalized to a thermalized regime on the time scales accessible to us. Increasing the integrability-breaking interactions leads to a behaviour that is compatible with eventual thermalization.

cond-mat.stat-mech↗

arXiv2013

Lindblad equation for a non-interacting fermionic system: full-counting statistics

We develop a method of calculating the full-counting statistics for a non-interacting fermionic system coupled to the memory-less reservoirs. The evolution of the system is described by the Lindblad equation. By the basis change the Liouvillian operator is brought to the quadratic form. This allows us a straightforward calculation of any observable in the non-equilibrium steady state. We introduce the counting field in the Lindblad equation which brings us to the generating function and helps us to obtain all cumulants of the charge transport. For the two-site system we give the expression for the generating function. For system longer than two sites we perform numerical investigations which suggest that it in a uniform system the cumulants of order $k$ are independent of the size of the system for system sizes larger $k+1$. The counting statistics from the Lindblad approach does not take into account interference in the reservoirs which gives a decreased noise in comparison with the Green function method which describes phase coherent leads. The current obtained by two methods is the same, which relies on the current conservation. The Fano factors are different (with a linear relation connecting them) and allow to distinguish between memory-less and phase coherent reservoirs.

cond-mat.mes-hall↗

arXiv2013

Spatiotemporal buildup of the Kondo screening cloud

We investigate how the Kondo screening cloud builds up as a function of space and time. Starting from an impurity spin decoupled from the conduction band, the Kondo coupling is switched on at time t=0. We work at the Toulouse point where one can obtain exact analytical results for the ensuing spin dynamics at both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts building up in the wake of the impurity spin being transported to infinity. In this buildup process the impurity spin--conduction band spin susceptibility shows a sharp light cone due to causality, while the corresponding correlation function has a tail outside the light cone. At T=0 this tail has a power law decay as a function of distance from the impurity, which we interpret as due to initial entanglement in the Fermi sea.

cond-mat.mes-hall↗

arXiv2011

Relaxation of hot electrons in a degenerate two-dimensional electron system: transition to one-dimensional scattering

The energy relaxation channels of hot electrons far from thermal equilibrium in a degenerate two-dimensional electron system are investigated in transport experiments in a mesoscopic three-terminal device. We observe a transition from two dimensions at zero magnetic field to quasi--one-dimensional scattering of the hot electrons in a strong magnetic field. In the two-dimensional case electron-electron scattering is the dominant relaxation mechanism, while the emission of optical phonons becomes more and more important as the magnetic field is increased. The observation of up to 11 optical phonons emitted per hot electron allows us to determine the onset energy of LO phonons in GaAs at cryogenic temperatures with a high precision, $\eph=36.0\pm0.1\,$meV. Numerical calculations of electron-electron scattering and the emission of optical phonons underline our interpretation in terms of a transition to one-dimensional dynamics.

cond-mat.mes-hall↗

arXiv2010

Scaling approach for the time-dependent Kondo model

We present a new nonperturbative method to deal with the time-dependent quantum many-body problem, which is an extension of Wegner's flow equations to time-dependent Hamiltonians. The formalism provides a scaling procedure for the set of time-dependent interaction constants. We apply these ideas to a Kondo model with a ferromagnetic exchange coupling switched on over a time scale $τ$. We show that the asymptotic expectation value of the impurity spin interpolates continuously between its quenched and adiabatic value.

cond-mat.str-el↗

arXiv2010

Electron-avalanche amplifier based on the electronic Venturi effect

Scattering of otherwise ballistic electrons far from equilibrium is investigated in a cold two-dimensional electron system. The interaction between excited electrons and the degenerate Fermi liquid induces a positive charge in a nanoscale region which would be negatively charged for diffusive transport at local thermal equilibrium. In a three-terminal device we observe avalanche amplification of electrical current, resulting in a situation comparable to the Venturi effect in hydrodynamics. Numerical calculations using a random phase approximation are in agreement with our data and suggest Coulomb interaction as the dominant scattering mechanism.

cond-mat.mes-hall↗

arXiv2010

Sudden interaction quench in the quantum sine-Gordon model

We study a sudden interaction quench in the weak-coupling regime of the quantum sine-Gordon model. The real time dynamics of the bosonic mode occupation numbers is calculated using the flow equation method. While we cannot prove results for the asymptotic long time limit, we can establish the existence of an extended regime in time where the mode occupation numbers relax to twice their equilibrium values. This factor two indicates a non-equilibrium distribution and is a universal feature of weak interaction quenches. The weak-coupling quantum sine-Gordon model therefore turns out to be on the borderline between thermalization and non-thermalization.

cond-mat.quant-gas↗

arXiv2010

New theoretical approaches for correlated systems in nonequilibrium

We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). In the nonequilibrium flow equation approach one first diagonalizes the Hamiltonian iteratively, performs the time evolution in this diagonal basis, and then transforms back to the original basis, thereby avoiding a direct perturbation expansion with errors that grow linearly in time. In nonequilibrium DMFT, on the other hand, the Hubbard model can be mapped onto a time-dependent self-consistent single-site problem. We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench. For the interaction quench in the Hubbard model, we have also obtained numerical DMFT results using quantum Monte Carlo simulations. In agreement with the flow equation approach they show that for weak coupling the system relaxes to a "prethermalized" intermediate state instead of rapid thermalization. We discuss the description of nonthermal steady states with generalized Gibbs ensembles.

cond-mat.str-el↗

arXiv2010

Non-equilibrium Scaling Properties of a Double Quantum Dot System: Comparison between Perturbative Renormalization Group and Flow Equation Approach

Since the experimental realization of Kondo physics in quantum dots, its far-from-equilibrium properties have generated considerable theoretical interest. This is due to the interesting interplay of non-equilibrium physics and correlation effects in this model, which has by now been analyzed using several new theoretical methods that generalize renormalization techniques to non-equilibrium situations. While very good agreement between these methods has been found for the spin-1/2 Kondo model, it is desirable to have a better understanding of their applicability for more complicated impurity models. In this paper the differences and commons between two such approaches, namely the flow equation method out of equilibrium and the frequency-dependent poor man's scaling approach are presented for the non-equilibrium double quantum dot system. This will turn out to be a particularly suitable testing ground while being experimentally interesting in its own right. An outlook is given on the quantum critical behavior of the double quantum dot system and its accessibility with the two methods.

cond-mat.str-el↗

arXiv2009

Non-Equilibrium Kondo Model with Voltage Bias in a Magnetic Field

We derive a consistent 2-loop scaling picture for a Kondo dot in both equilibrium and non-equilibrium situations using the flow equation method. Our analysis incorporates the important decoherence effects from both thermal and non-equilibrium noise in a common setting. We calculate the spin-spin correlation function, the T-matrix, and the magnetization as functions of applied magnetic field, dc-voltage bias and temperature. In all these quantities we observe characteristic non-equilibrium features for a nonvanishing external voltage bias like Kondo splitting and strongly enhanced logarithmic corrections.

cond-mat.str-el↗

arXiv2008

Unitary perturbation theory approach to real-time evolution problems

We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations of motion for an operator. It is our purpose to illustrate the accuracy of this approach by studying dissipative quantum systems on all time scales. In particular, we obtain results for non-equilibrium correlation functions for general initial conditions. We illustrate our ideas for the exactly solvable dissipative oscillator, and, as a non-trivial model, for the dissipative two-state system.

cond-mat.str-el↗

arXiv2008

Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.

cond-mat.str-el↗

arXiv2008

Interaction Quench in the Hubbard model

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: i) An initial buildup of correlations where the quasiparticles are formed. ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. iii) The long time limit described by a quantum Boltzmann equation leading to thermalization with a temperature T proportional to U.

cond-mat.str-el↗

arXiv2005

Unusual Non-Fermi Liquid Behavior of Ce$_{1-x}$La$_{x}$Ni$_{9}$Ge$_4$ Analyzed in a Single Impurity Anderson Model with Crystal Field Effects

CeNi$_{9}$Ge$_4$ exhibits unusual non-Fermi liquid behavior with the largest ever recorded value of the electronic specific heat $ΔC/T \cong 5.5$ JK$^{-2}$mol$^{-1}$ without showing any evidence of magnetic order. Specific heat measurements show that the logarithmic increase of the Sommerfeld coefficient flattens off below 200 mK. In marked contrast, the local susceptibility $Δχ$ levels off well above 200 mK and already becomes constant below 1 K. Furthermore, the entropy reaches 2$R$ln2 below 20 K corresponding to a four level system. An analysis of $C$ and $χ$ was performed in terms of an $SU(N=4)$ single impurity Anderson model with additional crystal electric field (CEF) splitting. Numerical renormalization group calculations point to a possible consistent description of the different low temperature scales in $Δc$ and $Δχ$ stemming from the interplay of Kondo effect and crystal field splitting.

cond-mat.str-el↗

arXiv2005

Violation of the Fluctuation-Dissipation Theorem and Heating Effects in the Time-Dependent Kondo Model

The fluctuation-dissipation theorem (FDT) plays a fundamental role in understanding quantum many-body problems. However, its applicability is limited to equilibrium systems and it does in general not hold in nonequilibrium situations. This violation of the FDT is an important tool for studying nonequilibrium physics. In this paper we present results for the violation of the FDT in the Kondo model where the impurity spin is frozen for all negative times, and set free to relax at positive times. We derive exact analytical results at the Toulouse point, and results within a controlled approximation in the Kondo limit, which allow us to study the FDT violation on all time scales.A measure of the FDT violation is provided by the effective temperature, which shows initial heating effects after switching on the perturbation, and then exponential cooling to zero temperature as the Kondo system reaches equilibrium.

cond-mat.str-el↗

arXiv2005

Crossover from Single-Ion to Coherent Non-Fermi Liquid Behavior in Ce$_{1-x}$La$_x$Ni$_9$Ge$_4$

We report specific heat and magneto-resistance studies on the compound Ce${}_{1-x}$La${}_x$Ni${}_9$Ge${}_4$ for various concentrations over the entire stoichiometric range. Our data reveal single-ion scaling with Ce-concentration between $x = 0.1$ and 0.95. Furthermore, CeNi${}_9$Ge${}_4$ turns out to have the largest ever recorded value of the electronic specific heat $Δc/T \approx$ 5.5 J $\rm K^{-2}mol^{-1}$ at $T=0.08$ K which was found in Cerium f-electron lattice systems. In the doped samples $Δc/T$ increases logarithmically in the temperature range between 3 K and 50 mK typical for non-Fermi liquid (nFl) behavior, while $ρ$ exhibits a Kondo-like minimum around 30 K, followed by a single-ion local nFl behavior. In contrast to this, CeNi${}_9$Ge${}_4$ flattens out in $Δc/T$ below 300 mK and displays a pronounced maximum in the resistivity curve at 1.5 K indicating a coherent heavy fermion groundstate. These properties render the compound Ce${}_{1-x}$La${}_x$Ni${}_9$Ge${}_4$ a unique system on the borderline between Fermi liquid and nFl physics.

cond-mat.str-el↗