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arXiv:2408.08194 · Physical review. B./Physical review. B

Two-doublon Bloch oscillations in the mass-imbalanced extended Fermi-Hubbard model

K. L. Zhang, Xunda Jiang, Yongyao Li

Published Nov 13, 2024• 5 citations
arXivHTMLPDF

Abstract

Interactions between particles normally induce the decay of the particles Bloch oscillations (BOs) in a periodic lattice. In the limit of strong on-site interactions, spin-$1/2$ fermions may form doublon bound states and undergo BOs in the presence of a tilted potential. Here we investigate the impact of nearest-neighbor interaction $V$ on the multidoublon BOs in a mass-imbalanced extended Fermi-Hubbard model. We derive an effective Hamiltonian for doublons, and show that a slight change in $V$ can qualitatively alter their dynamic behaviors. Notably, at a resonance point, the doublons behave like free hard-core bosons. Under a tilted potential, the system may exhibit different types of multidoublon BOs at or deviation from the resonance point. Numerical results are presented to demonstrate our conclusions in both one- and two-dimensional systems.

DOI
10.1103/physrevb.110.184304

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Interactions between particles normally induce the decay of the particles Bloch oscillations (BOs) in a periodic lattice. In the limit of strong on-site interactions, spin-1/21/21/2 fermions may form doublon bound states and undergo BOs in the presence of a tilted potential. Here we investigate the impact of nearest-neighbor interaction VVV on the multidoublon BOs in a mass-imbalanced extended Fermi-Hubbard model. We derive an effective Hamiltonian for doublons, and show that a slight change in VVV can qualitatively alter their dynamic behaviors. Notably, at a resonance point, the doublons behave like free hard-core bosons. Under a tilted potential, the system may exhibit different types of multidoublon BOs at or deviation from the resonance point. Numerical results are presented to demonstrate our conclusions in both one- and two-dimensional systems.
The onset of Bloch oscillations (BOs) for two correlated anyons hopping on a one-dimensional lattice is theoretically investigated in the framework of the anyon-Hubbard model. It is shown that, even in the absence of on-site particle interaction, BOs are degraded for a nonvanishing statistical phase exchange owing to the nonlocal quasiparticle nature of anyons. A remarkable exception is found for pseudofermions, i.e., particles that, although they are bosons on site, behave as fermions off site. In this case, if the ratio of forcing to the hopping rate is smaller than $\ensuremath{\sim}$0.50.50.5, in the absence of on-site interaction long-lived BOs are observed at a frequency which is half the BO frequency of single particles. This is notably distinct from results for previously investigated BOs of two strongly correlated bosons or fermions, in which particle correlation leads to a doubling of the BO frequency.
Two fermions occupying the same site of a lattice model with strongly repulsive Hubbard-type interaction UUU form a doublon, a long-living excitation, the decay of which is suppressed because of energy conservation. By means of an exact-diagonalization approach based on the Krylov-space technique, we study the dynamics of a single doublon, of two doublons, and of a doublon in the presence of two additional fermions prepared locally in the initial state of the extended Hubbard model. The time dependence of the expectation value of the double occupancy at the different sites of a large one-dimensional lattice is analyzed by perturbative arguments. In this way the spatiotemporal evolution of the doublon can be understood. The initial decay takes place on a short time scale 1/U1/U1/U, and the long-time average of the decayed fraction of the total double occupancy scales as 1/U21/{U}^{2}1/U2. We demonstrate how the dynamics of a doublon in the initial state is related to the spectrum of two-fermion excitations obtained from linear-response theory, we work out the difference between doublons composed of fermions vs doublons composed of bosons, and we show that despite the increase of phase space for inelastic decay processes, the stability of a doublon is enhanced by the presence of additional fermions on an intermediate time scale.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field are theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric Hubbard model shows that a high-frequency bichromatic external field can sustain a low-energy particle bound state (a doublon) in which two fermions of different species occupy nearest-neighbor sites and cotunnel along the lattice. The predictions of the asymptotic analysis are confirmed by direct numerical simulations of the two-particle Hubbard Hamiltonian.
It is known that there are lattice models in which noninteracting particles get dynamically localized when periodic $\ensuremath{\delta}$-function kicks are applied with a particular strength. We use both numerical and analytical methods to study the effects of interactions in three different models in one dimension. The systems we have considered include spinless fermions with interactions between nearest-neighbor sites, the Hubbard model of spin-1/2 fermions, and the Bose-Hubbard model with on-site interactions. We derive effective Floquet Hamiltonians up to second order in the time period of kicking. Using these we show that interactions can give rise to a variety of interesting results such as two-body bound states in all three models and dispersionless few-particle bound states with more than two particles for spinless fermions and bosons. We substantiate these results by exact diagonalization and stroboscopic time evolution of systems with a few particles. We derive a pseudo-spin-1/2 limit of the Bose-Hubbard system in the thermodynamic limit and show that a special case of this has an exponentially large number of degenerate eigenstates of the effective Hamiltonian. Finally, we study the effect of changing the strength of the $\ensuremath{\delta}$-function kicks slightly away from perfect dynamical localization; we find that a single particle remains dynamically localized for a long time after which it moves ballistically.
We investigate the possibility to control dynamically the interactions between repulsively bound pairs of fermions (doublons) in correlated systems with off-resonant ac fields. We introduce an effective Hamiltonian that describes the physics of doublons up to second order in the high-frequency limit. It unveils that the doublon interaction, which is attractive in equilibrium, can be completely suppressed and then switched to repulsive by varying the power of the ac field. We show that the signature of the dynamical repulsion between doublons can be found in the single-fermion density of states averaged in time. Our results are further supported by nonequilibrium dynamical mean-field theory simulations for the half-filled Fermi-Hubbard model.