Dynamical Phase Transitions and Non-Equilibrium States in the Kondo Lattice with Classical Spins

Benedikt Fauseweh, Jian‐Xin Zhu

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.

Ki‐Seok Kim, Mun Dae Kim

Andreas Hackl

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.

Ian P. McCulloch, M. Gulácsi, S. Caprara +2 more

Tokuro Hata

Igor Lesanovsky, Katarzyna Macieszczak, Juan P. Garrahan

We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a 1 + 1-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is separable. We show that for long times this state becomes stationary and displays a continuous phase transition in the density of excited spins. This phenomenon can be understood through a connection to the so-called Domany–Kinzel automaton, which implements a classical non-equilibrium process that features a transition to an absorbing state. Near the transition density–density correlations become long-ranged, and interestingly the same is the case for quantum correlations despite the separability of the stationary state. We quantify quantum correlations through the local quantum uncertainty and show that in some cases they may be determined experimentally solely by measuring expectation values of classical observables. This work is inspired by recent experimental progress in the realization of Rydberg lattice quantum simulators, which—in a rather natural way—permit the realization of conditional quantum gates underlying the discrete-time dynamics discussed here.