Abstract We investigate the non-equilibrium dynamics of the one-dimensional extended Hubbard model after interaction quenches. In strong-coupling regime with large on-site interaction, the ground states of this model with small and large nearest-neighbor interactions are in spin-density-wave and charge-density-wave phases, respectively. Combining twisted boundary conditions with the time-dependent Lanczos method, we obtain snapshots of the time-dependent single-particle spectrum after quenches. We find that for quench within the same phase, the single-particle spectrum becomes close to that of the quenched Hamiltonian immediately after the quench. While for quench across the critical point, the afterward evolution process depends mainly on the distribution of the initial state among the eigenstates of the quenched Hamiltonian. Our finding may serve as a way to detect the phase transition in ultracold atom systems with interactions.
Abstract We investigate the non-equilibrium dynamics of the one-dimensional extended Hubbard model after interaction quenches. In strong-coupling regime with large on-site interaction, the ground states of this model with small and large nearest-neighbor interactions are in spin-density-wave and charge-density-wave phases, respectively. Combining twisted boundary conditions with the time-dependent Lanczos method, we obtain snapshots of the time-dependent single-particle spectrum after quenches. We find that for quench within the same phase, the single-particle spectrum becomes close to that of the quenched Hamiltonian immediately after the quench. While for quench across the critical point, the afterward evolution process depends mainly on the distribution of the initial state among the eigenstates of the quenched Hamiltonian. Our finding may serve as a way to detect the phase transition in ultracold atom systems with interactions.
We investigate the short-time evolution of the half filled one-dimensional extended Hubbard model in the strong-coupling regime, driven by a transient laser pump. Combining twisted boundary conditions with the time-dependent Lanczos technique, we obtain snapshots of the single-particle spectral function with high momentum resolution. The analysis of the oscillations of the spectral function shows that its characteristic frequencies are consistent with the magnitudes of the optical gap. Furthermore, we examine the time-evolving spectral structure in the charge-density-wave phase in detail and find that one of the bands in the single-particle spectrum originates from the photoinduced bond-order background.
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.
Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, U and V, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on V. For small and intermediate values of V, both velocities increase with V. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by V. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.
In this paper, we study the nonequilibrium dynamics of the Bose–Hubbard model with the nearest-neighbor repulsion by using time-dependent Gutzwiller (GW) methods. In particular, we vary the hopping parameters in the Hamiltonian as a function of time, and investigate the dynamics of the system from the density wave (DW) to the superfluid (SF) crossing a first-order phase transition and vice versa. From the DW to SF, we find scaling laws for the correlation length and vortex density with respect to the quench time. This is a reminiscence of the Kibble–Zurek scaling for continuous phase transitions and contradicts the common expectation. We give a possible explanation for this observation. On the other hand from SF to DW, the system evolution depends on the initial SF state. When the initial state is the ground state obtained by the static GW methods, a coexisting state of the SF and DW domains forms after passing through the critical point. Coherence of the SF order parameter is lost as the system evolves. This is a phenomenon similar to the glass transition in classical systems. When the state starts from the SF with small local phase fluctuations, the system obtains a large size DW domain structure with thin domain walls.
Using the time-dependent Lanczos method, we study the nonequilibrium dynamics of the one-dimensional ionic-mass imbalanced Hubbard chain driven by a quantum quench of the on-site Coulomb interaction, where the system is prepared in the ground state of the Hamiltonian with a different Hubbard interaction. The exact diagonalization method (Lanczos algorithm) is adopted to study the zero temperature phase diagram in equilibrium, which is shown to be in good agreement with previous studies using density matrix renormalization group (DMRG). We then study the nonequilibrium quench dynamics of the spin and charge order parameters by fixing the initial and final Coulomb interactions while changing the quenching time protocols. Our study shows that the time evolution of the charge and spin order parameters strongly depend on the quenching time protocols. In particular, the effective temperature of the system will decrease monotonically as the quenching time is increased. By taking the final Coulomb interaction strength to be in the strong coupling regime, we find that the oscillation frequency of the charge order parameter increases monotonically with the Coulomb interaction. By contrast, the frequency of the spin order parameter decreases monotonically with increasing Coulomb interaction. We explain this result using an effective spin model and a two-site Hubbard model in the strong coupling limit. Finally, we take the final Coulomb interaction strength to be in the weak coupling regime and find that the oscillation frequency of both the charge and spin order parameters increases monotonically with decreasing Coulomb interaction. Our study suggests strategies to engineer the relaxation behavior of interacting quantum many-particle systems.
In the first part of this thesis we study the Aubry-André model for interacting fermions. We numerically describe its phase diagram at half filling, performing both DMRG and QMC simulations. We show the existence of a localized phase and other three regimes: luttinger liquid, charge density wave and productstate. We study the properties of the excited states of the Hamiltonian, looking for a many-body mobility edge in the spectrum, i.e. an energy threshold that separates localized from ergodic states. Analyzing many indicators we prove its existence. Finally we propose a quench-spectroscopy method for detecting the mobility edge dynamically. In the second part we study the expansion dynamics of two bosons in a one-dimensional lattice as ruled by the Bose-Hubbard model Hamiltonian, both in the attractive and repulsive regime. Using the Bethe Ansatz we identify the bound states effects and how the two-particles state evolves in time. We show that, independently from the initial state, there exists a strong relation between the expansion velocity and the presence of bound states in the spectrum. Moreover, we discuss the role of the lattice in the system expansion. In the third part we study the time evolution of the entanglement entropy in the Ising model, when it is dynamically driven across a quantum phase transition with different velocities. We computed the time-evolution of the half chain entanglement entropy and we found that, depending on the velocity at which the critical point is reached, it displays different regimes: an adiabatic one when the system evolves according to the instantaneous ground state; a a sudden quench regime when the system remains frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations. Moreover, we discuss the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.