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arXiv:cond-mat/0211099 · Physical review. B, Condensed matter

Numerical study of the E⊗e Jahn-Teller polaron and bipolaron

Samir El Shawish, J. Bonča, Li-Chung Ku, S. A. Trugman

Published Jan 10, 2003• 29 citations
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Abstract

The properties of the polaron and bipolaron are explored in the one-dimensional Jahn-Teller model with dynamical quantum phonons. The ground-state properties of the polaron and bipolaron are computed using a recently developed variational method. Dynamical properties of the ground state of a polaron are investigated by calculating the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega}).$ Our numerical results suggest that the Jahn-Teller and Holstein polarons are similar. However, in the strong-coupling regime qualitative differences in $\ensuremath{\sigma}(\ensuremath{\omega})$ between the two models are found and discussed. The influence of the electron-phonon coupling and the electrostatic repulsion on the bipolaron binding energy, bipolaron masses, and correlation functions is investigated.

DOI
10.1103/physrevb.67.014301

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The properties of the polaron and bipolaron are explored in the one-dimensional Jahn-Teller model with dynamical quantum phonons. The ground-state properties of the polaron and bipolaron are computed using a recently developed variational method. Dynamical properties of the ground state of a polaron are investigated by calculating the optical conductivity \ensuremathσ(\ensuremathω).\ensuremath{\sigma}(\ensuremath{\omega}).\ensuremathσ(\ensuremathω). Our numerical results suggest that the Jahn-Teller and Holstein polarons are similar. However, in the strong-coupling regime qualitative differences in \ensuremathσ(\ensuremathω)\ensuremath{\sigma}(\ensuremath{\omega})\ensuremathσ(\ensuremathω) between the two models are found and discussed. The influence of the electron-phonon coupling and the electrostatic repulsion on the bipolaron binding energy, bipolaron masses, and correlation functions is investigated.
We explore the properties of the bipolaron in a 1D Holstein-Hubbard model with dynamical quantum phonons. Using a recently developed variational method combined with analytical strong coupling calculations, we compute correlation functions, effective mass, bipolaron isotope effect and the phase diagram. The two site bipolaron has a significantly reduced mass and isotope effect compared to the on-site bipolaron, and is bound in the strong coupling regime up to twice the Hubbard U naively expected. The model can be described in this regime as an effective t-J-V model with nearest neighbor repulsion. These are the most accurate bipolaron calculations to date.
We explore the properties of the bipolaron in a 1D Holstein-Hubbard model with dynamical quantum phonons. Using a recently developed variational method combined with analytical strong coupling calculations, we compute correlation functions, effective mass, bipolaron isotope effect, and the phase diagram. The two site bipolaron has a significantly reduced mass and isotope effect compared to the on-site bipolaron, and is bound in the strong coupling regime up to twice the Hubbard U naively expected. The model can be described in this regime as an effective t-J-V model with nearest neighbor repulsion. These are the most accurate bipolaron calculations to date.
We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the one-dimensional polaron energy at intermediate coupling). We compute ground-state and low-lying excited-state properties of the model at continuous values of the wave vector k in essentially all parameter regimes. Our results for the polaron energy band, effective mass, and correlation functions compare favorably with those of other numerical techniques, including the density-matrix renormalization-group technique, the global-local method, and the exact diagonalization technique. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong-coupling perturbation theory.
The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.
A recently proposed variational approach based on an expansion in coherent states is used to investigate the single polaron features in the one-dimensional Holstein model. The method provides highly accurate results, both for static and dynamic properties, over a wide range of the polaron parameter space, from weak to strong coupling regimes, with a little numerical effort when compared with standard numerical techniques. The results for the spectral weight function and the real part of the optical conductivity are reported in the moderate adiabatic regime. We show that the spectral function exhibits a strong dependence on the polaron wave number kkk that is not present in the standard analytical approaches. The optical conductivity, in the strong coupling regime, displays a high-energy peak due to the photoionization of the small polaron, while, at lower energies, there is evidence of electronic transitions between localized states. These results show that the coherent-state basis is a very powerful basis to study interacting electron-phonon systems.
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.