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arXiv:1111.6722 · Physical Review B

Dissociation of a Hubbard-Holstein bipolaron driven away from equilibrium by a constant electric field

Denis Golež, J. Bonča, Lev Vidmar

Published Apr 12, 2012• 34 citations
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Abstract

Using a variational numerical method, we compute the time evolution of the Hubbard-Holstein bipolaron from its ground state when at $t=0$ the constant electric field is switched on. The system is evolved taking into account full quantum effects until it reaches a quasistationary state. In the zero-field limit, the current shows Bloch oscillations characteristic for the adiabatic regime where the electric field causes the bipolaron to evolve along the quasiparticle band. The bipolaron remains bound and the net current remains zero in this regime. At larger electric fields, the system enters the dissipative regime with a finite quasistationary current. Concomitantly, the bipolaron dissociates into two separate polarons. By examining different parameter regimes, we show that the appearance of a finite quasistationary current is inevitably followed by the dissociation of the bipolaron.

DOI
10.1103/physrevb.85.144304

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•Jan 1, 1998•0 citations
Using a variational numerical method, we compute the time evolution of the Hubbard-Holstein bipolaron from its ground state when at t=0t=0t=0 the constant electric field is switched on. The system is evolved taking into account full quantum effects until it reaches a quasistationary state. In the zero-field limit, the current shows Bloch oscillations characteristic for the adiabatic regime where the electric field causes the bipolaron to evolve along the quasiparticle band. The bipolaron remains bound and the net current remains zero in this regime. At larger electric fields, the system enters the dissipative regime with a finite quasistationary current. Concomitantly, the bipolaron dissociates into two separate polarons. By examining different parameter regimes, we show that the appearance of a finite quasistationary current is inevitably followed by the dissociation of the bipolaron.
This work represents a fundamental study of a Holstein polaron in one dimension driven away from the ground state by a constant electric field. Taking fully into account quantum effects, we follow the time evolution of the system from its ground state as the constant electric field is switched on at t=0t=0t=0 until it reaches a steady state. At weak electron-phonon coupling (EP), the system experiences damped Bloch oscillations (BO's) characteristic for a noninteracting electron band. An analytic expression of the steady-state current is proposed in terms of weak EP coupling and large electric field. For moderate values of EP coupling, the oscillations are almost critically damped and the system reaches the steady state after a short time. In the strong-coupling limit, weakly damped BO's, consistent with nearly adiabatic evolution within the polaron band, persist up to extremely large electric fields. A traveling polaron under the influence of the electric field leaves behind a trail of phonon excitations absorbing the excess energy gained from the electric field. The shape of the traveling polaron is investigated in detail.
The one-dimensional Holstein-Hubbard model with two electrons of opposite spin is studied using an extension of a recently developed quantum Monte Carlo method and a very simple yet rewarding variational approach, both based on a canonically transformed Hamiltonian. The quantum Monte Carlo method yields very accurate results in the regime of small but finite phonon frequencies, characteristic of many strongly correlated materials, e.g., the cuprates and the manganites. The influence of electron-electron repulsion, phonon frequency, and temperature on the bipolaron state is investigated. Thermal dissociation of the intersite bipolaron is observed at high temperatures, and its relation to an existing theory of the manganites is discussed.
The evolution of the properties of a finite density electronic system as a function of the electron-phonon coupling is investigated in the Holstein model using the dynamical mean-field theory (DMFT) that becomes exact in infinite dimensions. We compare the spinless fermion case, in which only isolated polarons can be formed, with the spinful model in which the polarons can bind and form bipolarons. In the latter case, the bipolaronic binding occurs within DMFT as a metal-insulator transition. In the adiabatic regime in which the phonon energy is small with respect to the electron hopping we compare numerically exact DMFT results with an analytical scheme inspired by the Born-Oppenheimer procedure. Within the latter approach, a truncation of the phononic Hilbert space leads to a mapping of the original model onto an Anderson spin-fermion model. In the anti-adiabatic regime (where the phonon energy exceeds the electronic scales) the standard treatment based on Lang-Firsov canonical transformation allows one to map the original model on to an attractive Hubbard model in the spinful case. The separate analysis of the two regimes supports the numerical evidence that the presence of well-defined polaronic lattice displacements is not necessarily associated to a metal-insulator transition, which is instead due to pairing between the carriers. The finite-dimensionality effects neglected in DMFT may lead to a finite conductivity in the bipolaronic state which is, however, not always associated with polaronic distortions. At the polaron crossover the Born-Oppenheimer approximation is shown to break down due to the entanglement of the electron-phonon state.
We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion UUU and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large UUU at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and UUU. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and∕or electron-electron interaction.
Characterizing bipolaron binding, and understanding how it depends on electron-phonon interaction, is crucial to unraveling the nature of emergent many-body states in strongly interacting electron-phonon systems. So far, most studies of bipolarons have been limited to the Holstein model, in which the coupling constant is momentum-independent. The paradigmatic example of momentum-dependent electron-phonon interaction comes from the system in which phonon distortions modify electron hopping, the SSH model. Already individual polarons in the SSH model are richer than the Holstein model counterparts, and feature a phase transition into the finite momentum ground state with increasing electron-phonon interaction. In this paper, we use a variational approach to study bipolarons in the one-dimensional SSH model and discuss their ground state, dispersion, and excitation spectra. We explore the full parameter range of the system, including the adiabatic regime of slow phonons, which was inaccessible to previous theoretical studies. In agreement with earlier studies, we find that in the anti-adiabatic strongly interacting regime, bipolarons have low effective mass. By contrast, in the adiabatic case, we find that increasing electron-phonon interactions results in an exponential increase of the bipolaron mass. We establish the existence of multiple branches of bound excited states of SSH bipolaron and discuss the signatures of these bound states in dynamics. We show that in the anti-adiabatic regime, response functions obey a parity selection rule, that imposes symmetry constraints on the excitation spectra and provides a clear signature of SSH bipolarons.
The bound states of two electrons in the adiabatic Holstein-Hubbard model are studied numerically in one and two dimensions from the anticontinuous limit. This model involves a competition between a local electron-phonon coupling (with a classical lattice) which tends to form pairs of electrons and the repulsive Hubbard interaction U≥0U \geq 0U≥0 which tends to break them. In 1D, the ground-state always consists in a pair of localized polarons in a singlet state. They are located at the same site for U=0. Increasing U, there is a first order transition at which the bipolaron becomes a spin singlet pair of two polarons bounded by a magnetic interaction. The pinning mode of the bipolaron soften in the vicinity of this transition leading to a higher mobility of the bipolaron which is tested numerically. In 2D, and for any UUU, the electron-phonon coupling needs to be large enough in order to form small polarons or bipolarons instead of extended electrons. We calculate the phase diagram of the bipolaron involving first order transitions lines with a triple point. A pair of polarons can form three types of bipolarons: a) on a single site at small UUU, b) a spin singlet state on two nearest neighbor sites for larger UUU as in 1D and c) a new intermediate state obtained as the resonant combination of four 2-sites singlet states sharing a central site, called quadrisinglet. The breathing and pinning internal modes of bipolarons in 2D generally only weakly soften and thus, they are practically not mobile. On the opposite, in the vicinity of the triple point involving the quadrisinglet, both modes exhibit a significant softening. However, it was not sufficient for allowing the existence of a classical mobile bipolaron (at least in that model).