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arXiv:cond-mat/0403751 · Physical Review Letters

Electron-Phonon Coupling and a Polaron in the t−J Model: From the Weak to the Strong Coupling Regime

Andrei S. Mishchenko, Naoto Nagaosa

Published Jul 12, 2004• 208 citations
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Abstract

We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for a single hole in the t-J model coupled to optical phonons. The systematic-error-free diagrammatic Monte Carlo method is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonon variables, while magnetic variables are subjected to the noncrossing approximation. We obtain that at electron-phonon coupling constants relevant for high T(c) cuprates the polaron undergoes a self-trapping crossover to the strong-coupling limit and theoretical ARPES demonstrate features observed in experiment: A broad peak in the bottom of the spectra has momentum dependence which coincides with that of a hole in the pure t-J model.

DOI
10.1103/physrevlett.93.036402

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•Jan 1, 2011•1 citation
We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for a single hole in the t-J model coupled to optical phonons. The systematic-error-free diagrammatic Monte Carlo method is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonon variables, while magnetic variables are subjected to the noncrossing approximation. We obtain that at electron-phonon coupling constants relevant for high T(c) cuprates the polaron undergoes a self-trapping crossover to the strong-coupling limit and theoretical ARPES demonstrate features observed in experiment: A broad peak in the bottom of the spectra has momentum dependence which coincides with that of a hole in the pure t-J model.
We present an efficient numerical method for the description of ground state and spectral properties of a doped hole in generalized $t\text{\ensuremath{-}}J$ models coupled to optical phonons. In the weak-coupling regime, coherent hole motion is less affected by the electron-phonon (EP) interaction in the electron than in the hole-doped system. Increasing the strength of EP coupling leads to a vanishing low-energy spectral weight around $\ensuremath{\Gamma}$ point. Spectral properties are in the strong coupling regime consistent with recent high-resolution angle resolved photoemission spectra (ARPES) [K. M. Shen et al., Phys. Rev. Lett. 93, 267002 (2004)]. A waterfall-like feature appears connecting the dispersive low-energy band with the incoherent high-energy peak resembling ARPES data [F. Ronning et al., Phys. Rev. B 71, 094518 (2005)].
We develop a novel self-consistent approach for studying the angle resolved photoemission spectra (ARPES) of a hole in the t-J Holstein model giving perfect agreement with numerically exact diagrammatic Monte Carlo (DMC) data at zero temperature for all regimes of electron-phonon coupling. Generalizing the approach to finite temperatures, we find that the anomalous temperature dependence of the ARPES in undoped cuprates is explained by cooperative interplay of coupling of the hole to magnetic fluctuations and strong electron-phonon interaction.
We present recent advances in understanding of the ground and excited states of the electron–phonon coupled systems obtained by novel methods of Diagrammatic Monte Carlo and Stochastic Optimization, which enable the approximation-free calculation of Matsubara Green function in imaginary times and perform unbiased analytic continuation to real frequencies. We analyze Rashba–Pekar exciton–polaron as a classic example of a system with self-trapping crossover and demonstrate basic features of the phenomenon. Analysis of unconventional self-trapping cases, such as Jahn–Teller driven crossover in one-dimensional systems and magnon-assisted localization in cuprates, is presented. Results on the optical conductivity of the Fröhlich polaron are also discussed.
We study thermal broadening of the hole spectral function of the two-dimensional $t\text{\ensuremath{-}}J$ model (and its extensions) within the noncrossing approximation (NCA) with and without the contribution of optical phonons. We find that phonons at finite temperature broaden the lowest energy quasiparticle peak, however, the string excitations survive even for relatively strong electron-phonon coupling. Experimental angle-resolved photoemission spectroscopy (ARPES) results compare well with our calculations at finite temperature when we use strong electron-phonon coupling without any ad hoc broadening. In addition, we have studied the role of vertex corrections and we find that their contribution allows us to achieve the same overall agreement with the ARPES experimental results but using smaller values for the electron-phonon coupling $(\ensuremath{\gamma}\ensuremath{\sim}0.5)$ than that required $(\ensuremath{\gamma}\ensuremath{\sim}1)$ when restricting ourselves within NCA.
We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by the diagrammatic Monte Carlo method and the data obtained through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.
Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.