We investigate the formation of charge and spin ordering by starting from a noninteracting state and studying how it evolves in time under a Hamiltonian with finite electronic interactions. We consider the one-dimensional, half-filled extended Hubbard model, which we solve within time-dependent density matrix renormalization group. By employing linear finite-time quenches in on-site and nearest-neighbor interactions, we find the existence of impulse, intermediate, and adiabatic regimes of time evolution. For the quenches we analyze, we observe that the adiabatic regime is reached with distinct ramping timescales depending on whether the charge density wave (CDW) or the spin density wave (SDW) is formed. The former needs to be slower than the latter to prevent entangled excited states from being accessed during the quench. More interestingly, in the intermediate regime, we observe an enhancement of the entanglement entropy with respect to its initial value, which precedes the formation of the CDW ordering; a similar enhancement is not seen in the quench toward SDW. Our findings also 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.
We investigate the formation of charge and spin ordering by starting from a noninteracting state and studying how it evolves in time under a Hamiltonian with finite electronic interactions. We consider the one-dimensional, half-filled extended Hubbard model, which we solve within time-dependent density matrix renormalization group. By employing linear finite-time quenches in on-site and nearest-neighbor interactions, we find the existence of impulse, intermediate, and adiabatic regimes of time evolution. For the quenches we analyze, we observe that the adiabatic regime is reached with distinct ramping timescales depending on whether the charge density wave (CDW) or the spin density wave (SDW) is formed. The former needs to be slower than the latter to prevent entangled excited states from being accessed during the quench. More interestingly, in the intermediate regime, we observe an enhancement of the entanglement entropy with respect to its initial value, which precedes the formation of the CDW ordering; a similar enhancement is not seen in the quench toward SDW. Our findings also 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.
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.
In this master’s dissertation, we explore non-equilibrium phenomena in strongly interacting electron systems. Our main focus is on investigating the emergence of charge and spin orderings in one-dimensional systems under non-equilibrium conditions. Starting from an initially disordered non-interacting state, we track its time evolution under an interacting Hamiltonian—a protocol known as a quantum quench. Specifically, we concentrate on the development of charge and spin orderings within the half-filled one-dimensional extended Hubbard model, characterized by repulsive interactions and exhibiting the charge density wave (CDW) and spin density wave (SDW) phases. We simulate the progression of the initial state under the Hamiltonian of the mentioned model, considering that the electronic interactions progressively scale up over a finite time interval, eventually reaching values corresponding to the CDW or SDW phase. The non-equilibrium dynamics are examined using the time-dependent extension of the density matrix renormalization group (t-DMRG) method, implemented through the ITensor software. Inspired by tensor diagrams, ITensor facilitates efficient and accurate numerical simulations, enabling comprehensive analyses of the system time evolution under different degrees of electronic interactions. After reproducing results obtained in our research group for the evolution during the quench, we proceed to investigate the post-quench free evolution. Analyzing the order parameters of the CDW and SDW phases, we identify three temporal regimes for the quenches: instantaneous, intermediate, and adiabatic. The system that achieved the adiabatic regime during the quench remained stable in the post-quench analysis. The system subject to the instantaneous regime during the quench did not converge to the ground state in the post-quench, exhibiting a significant increase in entropy. In the case of the intermediate regime, after reaching a peak during the quench, the parameters exhibited oscillatory behavior, which was also observed in larger chains.
We study the effects of a bond-charge interaction (or correlated hopping) on the properties of the extended [i.e., with both on-site (U) and nearest-neighbor (V) repulsions] Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, X, the charge-density-wave (CDW) state is more robust than the spin-density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when X=0. For X=t and fixed V2t (t is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponds to a different density of doubly occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any X in the range examined. \textcopyright{} 1996 The American Physical Society.
By employing the time-dependent Lanczos method, the nonequilibrium process of the half-filled one-dimensional extended Hubbard model under the irradiation of a transient laser pulse is investigated. We show that in the spin-density-wave (SDW) phase, the antiferromagnetic spin correlations are impaired by the photoinduced charge carriers. Near the phase boundary between the SDW and charge-density-wave (CDW) phases, a local enhancement of charge (spin) order that is absent in the original SDW (CDW) phase can be realized with proper laser frequency and strength. The possibility of restoration of spin orders from the CDW phase by optical means is discussed.
By using the density matrix renormalization group technique, the phase diagram of the half-filling extended Hubbard model is investigated. The conventional order parameter, the two-site entanglement entropy, and the block-block entanglement entropy are analyzed in detail. According to the numerical results, in the weak coupling region, an intermediate bond-order-wave (BOW) phase is shown to exist indeed between the charge-density-wave (CDW) and the spin-density-wave (SDW) phases. The critical phase transition points are determined by the singularity of the first order derivative of two-site entanglement entropy. In strong coupling region, a direct phase transition occurs from SDW phase to CDW phase, and shows discontinuous (first order) character accompanied with energy level crossing. The numerical results support the phase diagram proposed previously by some authors Sengupta et al., (2002); Sandvik et al., (2004); Zhang, (2004). Therefore, the quantum entanglement is a sensitive tool to describe quantum phase transitions in strongly correlated electron systems.
The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.