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.Comment: Final version as accepted for publication in Phys. Rev. B (4 pages, 3 figures

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.Comment: Final version as publishe

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 $\tau$. We show that the asymptotic expectation value of the impurity spin interpolates continuously between its quenched and adiabatic value

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.Comment: 18 pages, 4 figures, published in New Journal of Physic

Crossover from Non-Equilibrium to Equilibrium Behavior in the Time-Dependent Kondo Model

We investigate the equilibration of a Kondo model that is initially prepared in a non-equilibrium state towards its equilibrium behavior. Such initial non-equilibrium states can e.g. be realized in quantum dot experiments with time-dependent gate voltages. We evaluate the non-equilibrium spin-spin correlation function at the Toulouse point of the Kondo model exactly and analyze the crossover between non-equilibrium and equilibrium behavior as the non-equilibrium initial state evolves as a function of the waiting time for the first spin measurement. Using the flow equation method we extend these results to the experimentally relevant limit of small Kondo couplings.Comment: 4 pages, 2 figures; revised version contains added references and improved layout for figure

The Crooks relation in optical spectra - universality in work distributions for weak local quenches

We show that work distributions and non-equilibrium work fluctuation theorems can be measured in optical spectra for a wide class of quantum systems. We consider systems where the absorption or emission of a photon corresponds to the sudden switch on or off of a local perturbation. For the particular case of a weak local perturbation, the Crooks relation establishes a universal relation in absorption as well as in emission spectra. Due to a direct relation between the spectra and work distribution functions this is equivalent to universal relations in work distributions for weak local quenches. As two concrete examples we treat the X-ray edge problem and the Kondo exciton.Comment: 4+ pages, 1 figure; version as publishe

Non-equilibrium dynamics of a system with Quantum Frustration

Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is protected when the TLS is coupled symmetrically to both bath. A critical asymmetry angle separates the localized from the delocalized phase. On the other hand, real-time decoherence of a non-equilibrium initial state is for a generic initial state faster for a coupling to two baths than for a single bath.Comment: 22 pages, 9 figure

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.Comment: 10 pages, 9 figure

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 $\tau^{-3/2}$. This behaviour is universal and independent of the space dimension.Comment: 21 pages, 9 fig

Solving real time evolution problems by constructing excitation operators

In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are defined as the operators A satisfying [H,A]=\lambda A. It is demonstrated how an excitation operator and its excitation energy \lambda can be calculated. By an appropriate supposition of the form of A we turn the problem into the one of diagonalizing a series of matrices whose dimension depends linearly on the size of the system. We perform this method to calculate the evolution of the creation operator in a toy model Hamiltonian which is inspired by the Hubbard model and the nonequilibrium current through the single impurity Anderson model. This method is beyond the traditional perturbation theory in Keldysh-Green's function formalism, because the excitation energy \lambda is modified by the interaction and it will appear in the exponent in the function of time.Comment: 8 page