Excitons in the one-dimensional Hubbard model: a real-time study

Time-Dependent Variational Principle with Controlled Bond Expansion for Matrix Product States

We present a controlled bond expansion (CBE) approach to simulate quantum dynamics based on the time-dependent variational principle (TDVP) for matrix product states. Our method alleviates the numerical difficulties of the standard, fixed-rank one-site TDVP integrator by increasing bond dimensions on the fly to reduce the projection error. This is achieved in an economical, local fashion, requiring only minor modifications of standard one-site TDVP implementations. We illustrate the performance and accuracy of CBE-TDVP with several numerical examples on finite quantum lattices, including new results on bipolaron formation in the Peierls-Hubbard model and spin pumping via adiabatic flux insertion in a chiral spin liquid.

Dynamical Simulations of Carotenoid Photoexcited States Using Density Matrix Renormalization Group Techniques

We present a dynamical simulation scheme to model the highly correlated excited state dynamics of linear polyenes. We apply it to investigate the internal conversion processes of carotenoids following their photoexcitation. We use the extended Hubbard-Peierls model, H^UVP, to describe the π-electronic system coupled to nuclear degrees of freedom. This is supplemented by a Hamiltonian, H^ϵ, that explicitly breaks both the particle-hole and two-fold rotation symmetries of idealized carotenoid structures. The electronic degrees of freedom are treated quantum mechanically by solving the time-dependent Schrödinger equation using the adaptive time-dependent DMRG (tDMRG) method, while nuclear dynamics are treated via the Ehrenfest equations of motion. By defining adiabatic excited states as the eigenstates of the full Hamiltonian, H^=H^UVP+H^ϵ, and diabatic excited states as eigenstates of H^UVP, we present a computational framework to monitor the internal conversion process from the initial photoexcited 1¹B_u⁺ state to the singlet triplet-pair states of carotenoids. We further incorporate Lanczos-DMRG to the tDMRG-Ehrenfest method to calculate transient absorption spectra from the evolving photoexcited state. We describe in detail the accuracy and convergence criteria for DMRG, and show that this method accurately describes the dynamical processes of carotenoid excited states. We also discuss the effect of the symmetry-breaking term, H^ϵ, on the internal conversion process, and show that its effect on the extent of internal conversion can be described by a Landau-Zener-type transition. This methodological paper is a companion to our more explanatory discussion of carotenoid excited state dynamics in Manawadu, D.; Georges, T. N.; Barford, W. Photoexcited State Dynamics and Singlet Fission in Carotenoids. J. Phys. Chem. A 2023, 127, 1342.

Magnetic Doublon Bound States in the Kondo Lattice Model

We present a novel pairing mechanism for electrons, mediated by magnons. These paired bound states are termed "magnetic doublons." Applying numerically exact techniques (full diagonalization and the density-matrix renormalization group, DMRG) to the Kondo lattice model at strong exchange coupling J for different fillings and magnetic configurations, we demonstrate that magnetic doublon excitations exist as composite objects with very weak dispersion. They are highly stable, support a novel "inverse" colossal magnetoresistance and potentially other effects.

Ultrafast charge recombination in a photoexcited Mott-Hubbard insulator

We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates, which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in the picosecond range, can be explained even quantitatively with the multimagnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the s-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor, which can be traced back to strong correlations and consequently large exciton-magnon coupling.

Enhanced charge order in a photoexcited one-dimensional strongly correlated system

We present a compelling response of a low-dimensional strongly correlated system to an external perturbation. Using the time-dependent Lanczos method we investigate a nonequilibrium evolution of the half-filled one-dimensional extended Hubbard model, driven by a transient laser pulse. When the system is close to the phase boundary, by tuning the laser frequency and strength, a sustainable charge order enhancement is found that is absent in the Mott insulating phase. We analyze the conditions and investigate possible mechanisms of emerging charge order enhancement. Feasible experimental realizations are proposed.

Quantum dynamics of a driven correlated system coupled to phonons

Nonequilibrium interplay between charge, spin, and lattice degrees of freedom on a square lattice is studied for a single charge carrier doped in the t-J-Holstein model. In the presence of a static electric field we calculate the quasistationary state. With increasing electron-phonon (e-ph) coupling the carrier mobility decreases; however, we find increased steady state current due to e-ph coupling in the regime of negative differential resistance. We explore the distribution of absorbed energy between the spin and the phonon subsystem. For model parameters as relevant for cuprates, the majority of the gained energy flows into the spin subsystem.

Time evolution with the density-matrix renormalization-group algorithm: a generic implementation for strongly correlated electronic systems

A detailed description of the time-step-targeting time evolution method within the density-matrix renormalization-group algorithm is presented. The focus of this publication is on the implementation of the algorithm and its generic application. The case of one-site excitations within a Hubbard model is analyzed as a test for the algorithm, using open chains and two-leg ladder geometries. The accuracy of the procedure in the case of the recently discussed holon-doublon photo excitations of Mott insulators is also analyzed. Performance and parallelization issues are discussed. In addition, the full open-source code is provided as supplementary material.

Nonequilibrium quantum dynamics of a charge carrier doped into a Mott insulator

We study real-time dynamics of a charge carrier introduced into an undoped Mott insulator propagating under a constant electric field F on the t-J ladder and a square lattice. We calculate the quasistationary current. In both systems an adiabatic regime is observed followed by a positive differential resistivity (PDR) at moderate fields where the carrier mobility is determined. Quantitative differences between the ladder and two-dimensional (2D) systems emerge when at large fields both systems enter the negative differential resistivity (NDR) regime. In the ladder system Bloch-like oscillations prevail, while in two dimensions the current remains finite, proportional to 1/F. The crossover between the PDR and NDR in two dimensions is accompanied by a change of the spatial structure of the propagating spin polaron.