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.
Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: II. Linear Behavior in Neutral-to-Ionic Transition
Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: III. Interference Caused by a Double Pulse
Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: I. Threshold Behavior in Ionic-to-Neutral Transition
We study the Fermi-Hubbard model in the strongly correlated Mott phase under the influence of a harmonically oscillating electric field, e.g., a pump laser. In the Peierls representation, this pump field can be represented as an oscillating phase of the hopping rate $J(t)$, such that the effective time-averaged rate $\bar J$ is reduced, i.e., switching the pump laser suddenly is analogous to a quantum quench. Apart from this time-averaged rate $\bar J$, it is well known that the oscillating component of $J(t)$ can resonantly create particle-hole pairs if the pump frequency $ω_{\rm pump}$ equal…
We investigate the half-filled two-orbital Hubbard model with the crystalline electric field using dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. We systematically study how the interplay of the intra- and interorbital Coulomb interations together with the Hund coupling realizes the diagonal and off-diagonal ordered states. It is found that the antiferroorbital ordered state is realized in the Hubbard model, in addition to the antiferromagnetically ordered and excitonic states. The competition between the antiferroorbital ordered and excitonic st…
Highly intense electric field pulses can move the electronic momentum occupation in correlated metals over large portions of the Brillouin zone, leading to phenomena such as dynamic Bloch oscillations. Using the non-equilibrium fluctuation-exchange approximation for the two-dimensional Hubbard model, we study how such non-thermal electron-distributions drive collective spin and charge fluctuations. Suitable pulses can induce a highly anisotropic modification of the occupied momenta, and the corresponding spin dynamics results in a transient change from antiferromagnetic to anisotropic ferromag…
Calculation of conductivity in the Hubbard model is a challenging task. Recent years have seen much progress in this respect and numerically exact solutions are now possible in certain regimes. In this paper we discuss the calculation of conductivity for the square lattice Hubbard model in the presence of a perpendicular magnetic field, focusing on orbital effects. We present the relevant formalism in all detail and in full generality, and then discuss the simplifications that arise at the level of the dynamical mean field theory (DMFT). We prove that the Kubo bubble preserves gauge and transl…
Superconductivity and inhomogeneous charge-ordered state in the two-Dimensional Hubbard model -- Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model IV
The $U\rightarrow +\infty$ one-dimensional Hubbard model in an electric field has be exactly solved, with an emphasis on the charge current. It is found that undamped Bloch oscillations extensively exist in the system. Such conclusion has also been discussed for more general cases and we find that it is closely related to the temporal periodicity of the model Hamiltonian in electric field, rather than to the integrability of the model. As a comparison, we have also studied a model of electrons with $δ$-function interactions in continuous space, which is closely related to the Hubbard model, bu…
Moiré materials with flat electronic bands provide a highly controllable quantum system for studies of strong-correlation physics and topology. In particular, angle-aligned heterobilayers of semiconducting transition metal dichalcogenides (TMDs) with large band offset realize the single-band Hubbard models. Introduction of a new layer degree of freedom is expected to foster richer interactions, enabling Hund's physics, interlayer exciton condensation and new superconducting pairing mechanisms to name a few. Here, we report competing electronic orders in twisted AB-homobilayer WSe2, which reali…
Applying time-varying magnetic fields to Weyl metals, a pair of Weyl points become oscillating. This oscillating monopole and anti-monopole pair gives rise to AC Berry magnetic fields, responsible for the emergence of Berry electric fields, which have not been discussed before at least in the context of Weyl metals. Introducing this novel information into Boltzmann transport theory, we find anomalous Hall effects beyond Berry magnetic fields as a fingerprint of Berry electric fields.
We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency $Δk_F$ ($2Δk_F$). Here $Δk_F=π(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum spa…
We study prethermalization phenomena in weakly interacting Hubbard systems after electric-field pump pulses with finite duration. We treat the Hubbard interaction up to second order, applying the prethermalization paradigm for time-dependent interaction protocols, and the electric field strength beyond linear order. A scaling behavior with pulse duration is observed for the absorbed energy as well as individual prethermalized momentum occupation numbers, which we attribute to the leading quadratic orders in interaction and electric field. We show that a pronounced non-thermal momentum distribu…
We study the non-equilibrium response of a 4x3 Hubbard model at U=8 under the influence of a short electric field pulse, with the main focus on multiple photon excitations and on the change of double occupancy after the pulse. The behavior mainly depends on the driving frequency of the electric field. The largest change of double occupancy occurs during the pulse. For frequencies below the Mott gap, we observe multiphoton excitations at large field intensities. For frequencies beyond the gap energy, there is a region where Auger recombination reduces the double occupancy after the pulse. Impac…
Interchain coupling effects on photoinduced phase transitions between neutral and ionic phases in an extended Hubbard model with alternating potentials and an electron-lattice coupling
The electric and magnetic polarizations as well as the electric and magnetic susceptibilities of the Hubbard pair-cluster embedded in the external fields were studied by the exact method. Based on the grand canonical ensemble for open system, the numerical calculations were performed for the electron concentration corresponding to the half-filling case. It has been found that the electric and magnetic properties are strictly interrelated, what constitutes a manifestation of a magnetoelectric effect, and the detailed explanation of such behaviour was given. In particular, near the ground state …
The paper contains the discussion of the magnetocaloric and electrocaloric effect in a model dimer (pair cluster). The system of interest is modelled with a Hubbard Hamiltonian including the external electric and magnetic field. The thermodynamics of such pair is described exactly, on the grounds of the grand canonical ensemble, focusing on the half-filling of energy states. The quantities of interest, such as magnetic entropy, magnetic specific heat as well as isothermal entropy change resulting from the variation of either electric or magnetic field and appropriate Grüneisen ratios are calcu…
The chemical potential of the two-site Hubbard cluster (pair) embedded in the external electric and magnetic fields is studied by exact diagonalization of the Hamiltonian. The formalism of the grand canonical ensemble is adopted. The influence of temperature, Hubbard on-site Coulombic energy $U$ and electron concentration on the chemical potential is investigated and illustrated in figures. In particular, a discontinuous behaviour of the chemical potential (or electron concentration) in the ground state is discussed.
We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction $U$ is much larger than the hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_α,J_β,J_γ)$ on bonds …
