The electric-field response of a one-dimensional ring of interacting fermions, where the interactions are described by the extended Hubbard model, is investigated. By using an accurate real-time propagation scheme based on the Chebyshev expansion of the evolution operator, we uncover various nonlinear regimes for a range of interaction parameters that allows modeling of metallic and insulating (either charge density wave or spin density wave insulators) rings. The metallic regime appears at the phase boundary between the two insulating phases and provides the opportunity to describe either weakly or strongly correlated metals. We find that the fidelity susceptibility of the ground state as a function of magnetic flux piercing the ring provides a very good measure of the short-time response. Even completely different interacting regimes behave in a similar manner at short time scales as long as the ground-state fidelity susceptibility is the same. Depending on the strength of the electric field we find various types of responses: persistent currents in the insulating phase, a dissipative regime, or damped Bloch-like oscillations with varying frequencies or even irregular in nature. Furthermore, we also consider the dimerization of the ring and describe the response of a correlated band insulator. In this case the distribution of the energy levels is more clustered and the Bloch-like oscillations become even more irregular.
The electric-field response of a one-dimensional ring of interacting fermions, where the interactions are described by the extended Hubbard model, is investigated. By using an accurate real-time propagation scheme based on the Chebyshev expansion of the evolution operator, we uncover various nonlinear regimes for a range of interaction parameters that allows modeling of metallic and insulating (either charge density wave or spin density wave insulators) rings. The metallic regime appears at the phase boundary between the two insulating phases and provides the opportunity to describe either weakly or strongly correlated metals. We find that the fidelity susceptibility of the ground state as a function of magnetic flux piercing the ring provides a very good measure of the short-time response. Even completely different interacting regimes behave in a similar manner at short time scales as long as the ground-state fidelity susceptibility is the same. Depending on the strength of the electric field we find various types of responses: persistent currents in the insulating phase, a dissipative regime, or damped Bloch-like oscillations with varying frequencies or even irregular in nature. Furthermore, we also consider the dimerization of the ring and describe the response of a correlated band insulator. In this case the distribution of the energy levels is more clustered and the Bloch-like oscillations become even more irregular.
The time evolution properties of charge current for the one-dimensional Hubbard model in an electric field have been studied in a rigorous manner. We find that there is a complete and orthonormal set of time-evolution states for which the charge current can only keep zero or oscillate constantly, differing from the possible picture of damped or over-damped Bloch oscillations due to strong correlations. It is also found that, associated with these states, there is a set of constant phase factors, which are uniquely determined and are very useful on discussing the long-time evolution behaviors of the system.
Strongly correlated materials exhibit some of the most complex and technologically useful phenomena in condensed matter. We use the world line and determinant quantum Monte Carlo techniques to explore the phases of the Hubbard Hamiltonian, a model describing strong interactions, in a number of different contexts. We first consider the spin, charge, and bond order correlations of the one-dimensional extended fermion Hubbard model in the presence of a coupling to the lattice. A static alternating lattice distortion leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic, we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases. Second, we examine mixtures of bosons and fermions in one-dimensional optical lattices. We evaluate the density profiles and bosonic visibility [special characters omitted] resolving the discrepancy between theory and experiment by identifying parameter regimes where [special characters omitted] is reduced and increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that [special characters omitted] exhibits kinks which are tied to the domain evolution present in the pure bosonic case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments. Third, we report large scale calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the momentum distribution, allowing a more quantitative comparison with time-of-flight optical lattice experiments.
Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics, dynamical constraints, and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady-state DC transport regime and the role of dissipation in it, and electric-field-driven phase transitions. Despite tremendous efforts over the past decade employing various numerical and analytical approaches, the manner in which a nonequilibrium steady state gets established has remained an unresolved problem. We develop here an effective large-N Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power law in time, ultimately going over to an exponential decay beyond a large characteristic time ${\ensuremath{\tau}}_{d}$ that increases with N. Such a relaxation to a steady-state DC response is absent in the dissipation-free Hubbard chain at half filling. The steady-state current at small fields is governed by large-distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation-free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.
Abstract The time evolution properties of charge current for the one-dimensional Hubbard model in an electric field have been studied in a rigorous manner. We find that there is a complete and orthonormal set of time-evolution states for which the charge current can only keep zero or oscillate constantly, differing from the possible picture of damped or over-damped Bloch oscillations due to strong correlations. It is also found that, associated with these states, there is a set of constant phase factors, which are uniquely determined and are very useful on discussing the long-time evolution behaviors of the system.
Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly interacting fermions and incoherent bosons on a lattice. We consider a case where the particles are driven by a constant force, leading to the well-known Bloch oscillations, and we consider interactions that are weak enough not to overdamp these oscillations. This regime is computationally demanding and relevant for ultracold atoms in optical lattices. We derive a simple theory in terms of coupled dynamic equations for the particle density, energy density, current, and heat current, allowing for analytic solutions. As an application, we identify damping coefficients for Bloch oscillations in the Hubbard model at weak interactions and compute them for a one-dimensional toy model. We also approximately solve the long-time dynamics of a weakly interacting, strongly Bloch-oscillating cloud of fermionic particles in a tilted lattice, leading to a subdiffusive scaling exponent.
Abstract The nonlinear response behavior of 1D large-U charged Bose Hubbard model with a reduced Hamiltonian in electric field has been studied. By transforming the Hamiltonian into a tensor-state space introduced via auxiliary spinless-fermions and the sequence of empty- and doubly-occupied states along the lattice, we have discussed the time-evolution behavior of the system, and found that the charge current always shows Bloch oscillations. It is also found that higher-harmonic components, though small in magnitude, can appear in the corrected charge current.