The Dispersion Self-Energy of the Polaron.

The energy dispersion for arbitrary momentum of a polaron in n dimensions is calculated by the Rayleigh-Schr\"odinger perturbation theory and by a modified Brillouin-Wigner perturbation theory. For the energy and effective mass of the polaron ground state, both methods give results that agree with the results of V. V. Paranjape and P. V. Panjat [Phys. Rev. B 35, 2942 (1987)] to linear order in the polaron coupling constant \ensuremath{\alpha}. The self-energy shifts are progressively weakened with increasing dimension. In particular, this weakening occurs for the structure in the energy dispersion near the momentum value at which the polaron starts decaying via the emission of phonons.The energy dispersion for arbitrary momentum of a polaron in n dimensions is calculated by the Rayleigh-Schr\"odinger perturbation theory and by a modified Brillouin-Wigner perturbation theory. For the energy and effective mass of the polaron ground state, both methods give results that agree with the results of V. V. Paranjape and P. V. Panjat [Phys. Rev. B 35, 2942 (1987)] to linear order in the polaron coupling constant \ensuremath{\alpha}. The self-energy shifts are progressively weakened with increasing dimension. In particular, this weakening occurs for the structure in the energy dispersion near the momentum value at which the polaron starts decaying via the emission of phonons.

Physical review. B, Condensed matterDec 15, 198713 citations

Fermi-liquid behaviors in three-dimensional polaron system with tunable dispersion

Chen-Huan Wu

We investigate the electronic properties and electron correlations in a three-dimensional (3D) polaron system with tunable dispersion parameter in Fermi-liquid picture. The polaronic coupling is considered as a weakly attractive bare coupling. Both the single and many-polaron, zero and finite-temperature cases are considered in this paper. The physical quantities, including the self-energy, spectral function, optical conductivity (both the planar and 3D one), free energy, and momentum distribution function, are studied and are been verified exhibit Fermi-liquid features. Both the analytic derivation and numerical calculation are done in this paper to make our results reliable.We investigate the electronic properties and electron correlations in a three-dimensional (3D) polaron system with tunable dispersion parameter in Fermi-liquid picture. The polaronic coupling is considered as a weakly attractive bare coupling. Both the single and many-polaron, zero and finite-temperature cases are considered in this paper. The physical quantities, including the self-energy, spectral function, optical conductivity (both the planar and 3D one), free energy, and momentum distribution function, are studied and are been verified exhibit Fermi-liquid features. Both the analytic derivation and numerical calculation are done in this paper to make our results reliable.

arXiv:2004.09562Apr 20, 20200 citations

Single-polaron properties of the one-dimensional breathing-mode Hamiltonian

Bayo Lau, Mona Berciu, G. A. Sawatzky

We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave functions of the two lowest-energy eigenstates for any momentum, as well as a scheme to compute directly the polaron's Green's function. We contrast these results with the results for the 1D Holstein polaron. In particular, we find that the crossover from a large to a small polaron is significantly sharper. Unlike for the Holstein model, at moderate and large couplings, the breathing-mode polaron dispersion has nonmonotonic dependence on the polaron momentum $k$ . Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation.We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave functions of the two lowest-energy eigenstates for any momentum, as well as a scheme to compute directly the polaron's Green's function. We contrast these results with the results for the 1D Holstein polaron. In particular, we find that the crossover from a large to a small polaron is significantly sharper. Unlike for the Holstein model, at moderate and large couplings, the breathing-mode polaron dispersion has nonmonotonic dependence on the polaron momentum $k$. Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation.

arXiv:0708.2920Physical Review BNov 21, 200730 citations

On the ground state energy of a polaron

K Chakraborty

Chemical Physics LettersAug 1, 19740 citations

k

. Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation.