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Journal of Physics Conference Series

Nonlinear Response of 1D Large-U Charged Bose Hubbard Model in Electric Field

Yong Zheng

Published Mar 1, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/2470/1/012014

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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.
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.
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.
Nonlinear real-time response of interacting particles is studied on the example of a one-dimensional tight-binding model of spinless fermions driven by electric field. Using equations of motion and numerical methods we show that for a nonintegrable case at finite temperatures the major effect of nonlinearity can be taken into account within the linear response formalism extended by a renormalization of the kinetic energy due to the Joule heating. On the other hand, integrable systems show on constant driving a different universality with a damped oscillating current whereby the frequency is related but not equal to the Bloch oscillations.
We theoretically investigate Bloch oscillations in a one-dimensional Bose–Hubbard chain, with single-particle losses from the odd lattice sites described by a Lindblad equation. For a single particle the time evolution of the state is completely determined by a non-Hermitian effective Hamiltonian. We analyse the spectral properties of this Hamiltonian for an infinite lattice and link features of the spectrum to observable dynamical effects, such as frequency doubling in breathing modes. We further consider the case of many particles in the mean-field limit leading to complex nonlinear Schrödinger dynamics. Analytic expressions are derived for the generalised nonlinear stationary states and the nonlinear Bloch bands. The interplay of nonlinearity and particle losses leads to peculiar features in the nonlinear Bloch bands, such as the vanishing of solutions and the formation of additional exceptional points. The stability of the stationary states is determined via the Bogoliubov–de Gennes equation and is shown to strongly influence the mean-field dynamics. Remarkably, even far from the mean-field limit, the stability of the nonlinear Bloch bands appears to affect the quantum dynamics. This is demonstrated numerically for a two-particle system.