Quenches em sistemas interagentes unidimensionais: formação de ordenamentos de carga e spin

Abstract

In this thesis, we study non-equilibrium phenomena in strongly interacting systems. We focus on the out-of-equilibrium formation of charge and spin ordering in one dimension, starting from a disordered non-interacting state and that we let evolve in time according to an interacting Hamiltonian. We analyze the formation of charge and spin ordering within the half-filled one-dimensional extended Hubbard model with repulsive interactions, which presents the charge density wave (CDW) and spin density wave (SDW) phases. We perform finite time quenches to simulate the evolution of the initial state under a Hamiltonian in which electronic interactions increase linearly in time up to final values corresponding to the CDW or SDW phase. The non-equilibrium dynamics is described by the time extension of the density matrix renormalization group (DMRG) method.

By linearly turning on the nearest-neighbor or the onsite interaction, we describe the formation of the CDW and SDW ordering, respectively. Our analysis is based on the behavior, along the quench, of the CDW and SDW order parameters, the entanglement entropy, and the fidelity between the evolved state and the corresponding equilibrium ground state. We classify the system behaviour according to the timescale in which the quench is performed: we find the existence of impulse, intermediate, and adiabatic regimes. During the quench, in the impulse regime, we observe that the evolved state remains in the same configuration as the initial state, while in the adiabatic regime it follows the predicted behavior for the ground state of the instantaneous Hamiltonian. For the quenches we analyze, our results indicate that the timescale associated with adiabatic behavior depends on the final state ordering. We observe that the adiabatic regime is reached more slowly when the final state has CDW ordering, compared to the case in which the final state has spin ordering. In the intermediate regime, preceding the adiabatic one in the first case we see an increase in entanglement entropy beyond its initial value which is not observed in the quench towards SDW. We conclude that the adiabatic regime for the case of CDW ordering requires a longer time to prevent entangled excited states from being accessed during the quench. In our work, we also compare cases in which only one of the interactions (onsite or nearest-neighbor) is turned on during the quench with those in which we turn on both interactions simultaneously. Our findings show that the breaking of the system integrability, by turning on the nearest-neighbor interactions, does not give rise to significant changes in the nonequilibrium behavior within the adiabatic approximation.