We provide a theoretical framework to describe the nonequilibrium temporal dynamics of correlated electron systems for realistic system parameters and the consequent, often exponentially long timescales. It is based on an entirely integrodifferential formulation of time-dependent dynamical mean-field theory, the noncrossing approximation, and the quantum representation of a driving electromagnetic field. For heavy-fermion systems, we identify two key nonequilibrium mechanisms governing their time evolution after a single-cycle terahertz excitation: transient, instantaneous shift from the Kondo toward the mixed-valence regime by an enhanced, photo-assisted hybridization, and slow recovery of the heavy-fermion state due to the long Kondo coherence time. This explains recent time-resolved terahertz spectroscopy experiments microscopically and establishes the latter as a technique for direct experimental access to the Kondo coherence time and to the heavy-fermion quasiparticle weight, central for the classification of heavy-fermion quantum phase transitions.
We provide a theoretical framework to describe the nonequilibrium temporal dynamics of correlated electron systems for realistic system parameters and the consequent, often exponentially long timescales. It is based on an entirely integrodifferential formulation of time-dependent dynamical mean-field theory, the noncrossing approximation, and the quantum representation of a driving electromagnetic field. For heavy-fermion systems, we identify two key nonequilibrium mechanisms governing their time evolution after a single-cycle terahertz excitation: transient, instantaneous shift from the Kondo toward the mixed-valence regime by an enhanced, photo-assisted hybridization, and slow recovery of the heavy-fermion state due to the long Kondo coherence time. This explains recent time-resolved terahertz spectroscopy experiments microscopically and establishes the latter as a technique for direct experimental access to the Kondo coherence time and to the heavy-fermion quasiparticle weight, central for the classification of heavy-fermion quantum phase transitions.
Ultrafast laser pulse has provided a systematic way to inspect the dynamics of electrons in condensed matter systems. In this paper, by means of time-dependent density matrix renormalization group, we study an ultrafast laser-driven Kondo lattice model, in which conduction electrons are strongly coupled with magnetically local moments. The single-particle spectral function due to strong correlation effects and photon emission in the nonequilibrium states under laser driving are calculated. We find laser field excited collective doublon-hole pairs and an associated transient melting of Kondo coherence phase, signifying the collapse of Kondo energy gap. Moreover, we show that the photon emission, induced by a strong laser field, exhibits a different intensity characteristics than in the equilibrium Kondo insulator, which could be explained by the Kondo collapse and related suppression of both intraband and interband contribution in Kondo melting liquid. This theoretical insight is accessible with time- and angle-resolved photoemission spectroscopy and high-harmonic generation spectroscopy and will stimulate the investigation of nonequilibrium dynamics and nonlinear phenomenon in heavy fermion systems.
We study the relaxation properties of the Kondo lattice model using the nonequilibrium dynamical mean-field formalism in combination with the noncrossing approximation. The system is driven out of equilibrium either by a magnetic field pulse, which perturbs the local singlets, or by a sudden quench of the Kondo coupling. For relaxation processes close to thermal equilibrium (after a weak perturbation), the relaxation time increases substantially as one crosses from the local moment regime into the heavy Fermi liquid. A strong perturbation, which injects a large amount of energy, can rapidly transform the heavy Fermi liquid into a local moment state. Upon cooling, the heavy Fermi liquid reappears in a two-stage relaxation, where the first step opens the Kondo gap and the second step corresponds to a slow approach of the equilibrium state via a nonthermal pathway.
Abstract When a system close to a continuous phase transition is subjected to perturbations, it takes an exceptionally long time to return to equilibrium. This critical slowing down is observed universally in the dynamics of bosonic excitations, such as order-parameter collective modes, but it is not generally expected to occur for fermionic excitations. Here using terahertz time-domain spectroscopy, we find evidence for fermionic critical slowing down in YbRh2Si2 close to a quantum phase transition between an antiferromagnetic phase and a heavy Fermi liquid. In the latter phase, the relevant quasiparticles are a quantum superposition of itinerant and localized electronic states with a strongly enhanced effective mass. As the temperature is lowered on the heavy-Fermi-liquid side of the transition, the heavy-fermion spectral weight builds up until the Kondo temperature TK ≈ 25 K, then decays towards the quantum phase transition and is, thereafter, followed by a logarithmic rise of the quasiparticle excitation rate below 10 K. A two-band heavy-Fermi-liquid theory shows that this is indicative of the fermionic critical slowing down associated with heavy-fermion breakdown near the quantum phase transition. The critical exponent of this breakdown could be used to classify this system among a wider family of fermionic quantum phase transitions that is yet to be fully explored.
Fast and dynamical control of quantum phases is highly desired in the application of quantum phenomena in devices. On the experimental side, ultrafast laser pulses provide an ideal platform to induce femtosecond dynamics in a variety of materials. Here we show that a laser pulse driven heavy fermion system can be tuned to dynamically evolve into a phase, which is not present in equilibrium. Using the state-of-the-art time-dependent variational Monte Carlo method, we perform numerical simulations of realistic laser pulses applied to the Kondo lattice model. By tracking spin and charge degrees of freedom we identify a dynamical phase transition, within the partially Kondo screened phase, from a charge ordered into a metallic state, while preserving the spin order of the system. We propose using high-harmonic generation and nonequilibrium optical conductivity to identify the dynamical phase transition in an ultrafast experiment.
A detailed derivation of the recently proposed time-dependent numerical renormalization-group (TD-NRG) approach to nonequilibrium dynamics in quantum-impurity systems is presented. We demonstrate that the method is suitable for fermionic as well as bosonic baths. Comparisons with exact analytical results for the charge relaxation in the resonant-level model and for dephasing in the spin-boson model establish the accuracy of the method. The real-time dynamics of a single spin coupled to each type of bath is investigated. We use the TD-NRG to calculate the spin relaxation and spin precession of a single Kondo impurity. The short- and long-time dynamics are studied as a function of temperature in the ferromagnetic and antiferromagnetic regimes. The short-time dynamics agrees very well with analytical results obtained at second order in the exchange coupling J. In the ferromagnetic regime, the transient spin decay is described by the scaling variable $x=2{\ensuremath{\rho}}_{F}\ensuremath{\mid}J(T)\ensuremath{\mid}Tt$. In the antiferromagnetic regime, the long-time decay is governed for T<TK by the Kondo time scale 1∕TK. Here ${\ensuremath{\rho}}_{F}$ is the conduction-electron density of states, TK is the Kondo temperature, and J(T) is the effective exchange coupling at temperature T. Results for spin precession are obtained by rotating the external magnetic field from the x axis to the z axis.
In this thesis, several cases of non-equilibrium phenomena and quantum phase transitions in strongly correlated electron systems are analyzed. The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals has triggered proposals on the breakdown of the Kondo effect at the critical point. In part I, we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling � this model displays both Kondo volume collapse and Kondo-breakdown transitions. Within a large-N treatment, we find that the Kondo breakdown transition remains of second order except for very soft lattices. Finally, we relate our findings to current heavy-fermion experiments. Using non-equilibrium Green�s functions, we derive transport equations for the degrees of freedom participating in the quantum critical region of the Kondo breakdown transition. We discuss conditions under which the transport of electrical charge is described by the independent motion of conduction electrons and auxiliary bosons. Under these conditions, we derive a semiclassical transport equation for the bosons and quantitatively discuss the electrical conductivity of the whole system. Motivated by pressure experiments on FeAs-122 superconductors, in part II we propose a scenario based on local-moment physics to explain salient features at the magnetic phase boundary of CaFe2As2. In this scenario, the low-pressure magnetic phase derives from Fe moments, which become screened in the paramagnetic high-pressure phase. The quantum phase transition can be described as an orbital-selective Mott transition, which is rendered first order by coupling to the lattice. These ideas are illustrated by a suitable mean-field analysis of an Anderson lattice model. An analytical description of non-equilibrium phenomena in interacting quantum systems is rarely possible. In part III we present one example where such a description can be achieved, namely the ferromagnetic Kondo model. In equilibrium, this model is tractable via perturbative renormalization-group techniques. We employ a recently developed extension of the flow-equation method to calculate the non-equilibrium decay of the local magnetization at zero temperature. The flow equations admit analytical solutions which become exact at short and long times, in the latter case revealing that the system always retains a memory of its initial state. Finally, in part IV we analyze the Nernst effect resulting from normal state quasiparticles in the cuprates in presence of various types of translational symmetry breaking. In the electron-doped cuprates, the Nernst signal resulting from a reconstruction of the Fermi surface due to spin density wave order is discussed. An order parameter consistent with the reconstruction of the Fermi surface detected in electron-doped materials is shown to sharply enhance the Nernst signal close to optimal doping. Within a semiclassical treatment, the obtained magnitude and position of the enhanced Nernst signal agrees with Nernst measurements in electron-doped cuprates. In the hole-doped cuprates, we discuss relations between the normal-state Nernst effect and stripe order. We find that Fermi pockets caused by translational symmetry breaking lead to a strongly enhanced Nernst signal with a sign depending on the modulation period of the ordered state and other details of the Fermi surface. This implies differences between antiferromagnetic and charge-only stripes. We compare our findings with recent data from La1.6−xNd0.4SrxCuO4 and YBa2Cu3Oy.