Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2011.07220

Oscillating charge currents of one-dimensional Hubbard model in an electric field

Zheng Yong

Published Nov 14, 2020• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2011.07220

Related papers

Oscillating charge currents of one-dimensional Hubbard model in electric field

Yong Zheng

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.

Journal of Physics Conference Series•Jul 1, 2022•0 citations

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

Yong Zheng

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.

Journal of Physics Conference Series•Mar 1, 2023•0 citations

Damping of Bloch Oscillations in the Hubbard Model

Martin Eckstein, Philipp Werner

Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a critical value, below which the system exhibits an ac-type response with Bloch oscillations. The transition from ac to dc response is defined in terms of the universal long-time behavior of the system, which does not depend on the initial condition.

arXiv:1107.3830•Physical Review Letters•Oct 27, 2011•75 citations

Nonlinear response to electric field in extended Hubbard models

Davoud Nasr Esfahani, Lucian Covaci, François Maria Peeters

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.

arXiv:1404.3529•Physical Review B•Nov 14, 2014•6 citations

Current characteristics of a one-dimensional Hubbard chain: Role of correlation and dissipation

Jakob Neumayer, Enrico Arrigoni, Markus Aichhorn +1 more

We study the electronic transport in an infinite one-dimensional Hubbard chain, driven by a homogeneous electric field. The physical chain is coupled to fermionic bath chains in order to account for dissipation and to prevent the occurrence of Bloch oscillations. The steady-state current is computed in the frame of Keldysh Green's functions in cluster perturbation theory. The current characteristics are dominated by resonant-tunneling-like structures, which can be traced back to Wannier-Stark resonances due to antiferromagnetic correlations. The same current characteristic occurs in a noninteracting Wannier-Stark model with alternating on-site energies. Nonlocal effects of the self-energy can be accounted for the observed physical behavior.

arXiv:1506.04957•Physical Review B•Sep 29, 2015•15 citations

Generalized hydrodynamic approach to charge and energy currents in the one-dimensional Hubbard model

Yuji Nozawa, Hirokazu Tsunetsugu

We have studied nonequilibrium dynamics of the one-dimensional Hubbard model using the generalized hydrodynamic theory. We mainly investigated the spatiotemporal profile of particle density (equivalent to charge density), energy density, and their currents using the partitioning protocol; the initial state consists of two semi-infinite different thermal equilibrium states joined at the origin. In this protocol, a transient region where currents flow appears around the origin, and this region expands its size linearly with time. We examined how density and current profiles depend on initial conditions. Inside the transient region, we have found a clogged region where charge current is zero but nonvanishing energy current flows. This phenomenon is similar to spin-charge separation in Tomonaga-Luttinger liquids, in which spin and charge excitations propagate with different velocities. This region appears when one of the initial states has half-filled electron density, and it is located adjacent to this initial state. We have proved analytically the existence of the clogged region in the infinite temperature case of the half-filled initial state. The existence is confirmed also for finite temperatures by numerical calculations of generalized hydrodynamics. A similar analytical proof is also given for a clogged region of spin current when magnetic field is applied to one and only one of the two initial states. A universal proportionality of charge and spin currents is also proved for a special region, for general initial conditions of electron density and magnetic field. To examine the clogged region of charge current, we have calculated the current contributions of different types of quasiparticles in the Hubbard model. It is found that the charge current component carried by scattering states (i.e., Fermi liquid type) is canceled completely in the clogged region by the counter flows carried by bound-state quasiparticles (called $k\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ strings). Their contributions are not canceled for energy current, which is also proved analytically for special cases, and these different behaviors are the origin of the clogged region. Except for the clogged region, charge and energy densities are in good proportion to each other, and their ratio depends on the initial conditions. This proportionality, in nonequilibrium dynamics, is reminiscent of Wiedemann-Franz law in thermal equilibrium, which states current proportionality determined by temperature. The long-time stationary values of charge and energy currents were also studied with varying initial conditions. We have compared the results with the values of noninteracting systems and discussed the effects of electron correlations. The ratio of these stationary currents is also analyzed. We have found that the temperature dependence of the ratio is strongly suppressed by electron correlations and even reversed.

arXiv:1910.02427•Physical review. B./Physical review. B•Jan 13, 2020•32 citations
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.
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.
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.
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.
We study the electronic transport in an infinite one-dimensional Hubbard chain, driven by a homogeneous electric field. The physical chain is coupled to fermionic bath chains in order to account for dissipation and to prevent the occurrence of Bloch oscillations. The steady-state current is computed in the frame of Keldysh Green's functions in cluster perturbation theory. The current characteristics are dominated by resonant-tunneling-like structures, which can be traced back to Wannier-Stark resonances due to antiferromagnetic correlations. The same current characteristic occurs in a noninteracting Wannier-Stark model with alternating on-site energies. Nonlocal effects of the self-energy can be accounted for the observed physical behavior.
We have studied nonequilibrium dynamics of the one-dimensional Hubbard model using the generalized hydrodynamic theory. We mainly investigated the spatiotemporal profile of particle density (equivalent to charge density), energy density, and their currents using the partitioning protocol; the initial state consists of two semi-infinite different thermal equilibrium states joined at the origin. In this protocol, a transient region where currents flow appears around the origin, and this region expands its size linearly with time. We examined how density and current profiles depend on initial conditions. Inside the transient region, we have found a clogged region where charge current is zero but nonvanishing energy current flows. This phenomenon is similar to spin-charge separation in Tomonaga-Luttinger liquids, in which spin and charge excitations propagate with different velocities. This region appears when one of the initial states has half-filled electron density, and it is located adjacent to this initial state. We have proved analytically the existence of the clogged region in the infinite temperature case of the half-filled initial state. The existence is confirmed also for finite temperatures by numerical calculations of generalized hydrodynamics. A similar analytical proof is also given for a clogged region of spin current when magnetic field is applied to one and only one of the two initial states. A universal proportionality of charge and spin currents is also proved for a special region, for general initial conditions of electron density and magnetic field. To examine the clogged region of charge current, we have calculated the current contributions of different types of quasiparticles in the Hubbard model. It is found that the charge current component carried by scattering states (i.e., Fermi liquid type) is canceled completely in the clogged region by the counter flows carried by bound-state quasiparticles (called $k\text{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}$ strings). Their contributions are not canceled for energy current, which is also proved analytically for special cases, and these different behaviors are the origin of the clogged region. Except for the clogged region, charge and energy densities are in good proportion to each other, and their ratio depends on the initial conditions. This proportionality, in nonequilibrium dynamics, is reminiscent of Wiedemann-Franz law in thermal equilibrium, which states current proportionality determined by temperature. The long-time stationary values of charge and energy currents were also studied with varying initial conditions. We have compared the results with the values of noninteracting systems and discussed the effects of electron correlations. The ratio of these stationary currents is also analyzed. We have found that the temperature dependence of the ratio is strongly suppressed by electron correlations and even reversed.