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arXiv:2005.12812 · Physical review. B./Physical review. B

Dynamically induced doublon repulsion in the Fermi-Hubbard model probed by a single-particle density of states

V. N. Valmispild, C. Dutreix, Martin Eckstein, Mikhail I. Katsnelson, Alexander I. Lichtenstein, E. A. Stepanov

Published Dec 2, 2020• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.102.220301

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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.
We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive. The nonadiabatically driven system is characterized by a negative temperature with a population inversion. We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method. Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.
We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive.The nonadiabatically driven system is characterized by a negative temperature with a population inversion.We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method.Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.
Abstract For the Mott insulator state of the Fermi-Hubbard model in the strong-coupling limit, we study the interaction between quasi-particles in the form of doublons and holons. Comparing different methods – the hierarchy of correlations, strong-coupling perturbation theory, and exact analytic solutions for the Hubbard tetramer – we find an effective interaction between doublons and/or holons to linear order in the hopping strength which can display attractive as well as repulsive contributions, depending on the involved momenta. Finally, we speculate about the implications of our findings for high-temperature superconductivity.
We investigate the dynamics of bound pairs in an extended Hubbard model at resonance. We show that a single fermion and a singlet bound pair possess identical dispersion relations and scatter off each other. In contrast, a neighboring doublon pair is dynamically pinned in the strong-interaction regime. Remarkably, a single fermion and a singlet bound pair exhibit fundamentally different scattering behaviors when encountering a pinned doublon pair acting as a scattering center. While the singlet bound pair undergoes perfect transmission, the single fermion is completely reflected. These results demonstrate that a neighboring doublon pair functions as an efficient filter that separates bound pairs from single particles. Numerical simulations fully support the analytical predictions. Our findings provide a dynamical mechanism for generating and manipulating bound-pair states.
In the strongly interacting limit of the Hubbard model localized double occupancies form effective hard-core bosonic excitations, called doublons, which are long lived due to energy conservation. Using time-dependent density-matrix renormalization group methods we investigate numerically the dynamics of doublons arising from the sudden expansion of a spatially confined band-insulating state in one spatial dimension. By analyzing the occupation scaling of the natural orbitals within the many-body state, we show that doublons dynamically quasicondense at the band edges, consistent with the spontaneous emergence of an $\ensuremath{\eta}$ quasicondensate. Building on this, we study the effect of periodically driving the system during the expansion. Floquet analysis reveals that doublon hopping and doublon repulsion are strongly renormalized by the drive, breaking the $\ensuremath{\eta}\text{\ensuremath{-}}\mathrm{SU}(2)$ symmetry of the Hubbard model. Numerical simulation of the driven expansion dynamics demonstrates that the momentum in which doublons quasicondense can be controlled by the driving amplitude. These results point to new pathways for engineering nonequilibrium condensates in fermionic cold-atom experiments and are potentially relevant to driven solid-state systems.
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.