Many-Polaron Effects in the Holstein Model

Abstract

We derive an effective polaronic interaction Hamiltonian, {\it exact to second order in perturbation}, for the spinless one-dimensional Holstein model. The small parameter is given by the ratio of the hopping term ($t$) to the polaronic energy ($g^2{\omega }_0$) in all the region of validity for our perturbation; however, the exception being the regime of extreme anti-adiabaticity ($t/{\omega }_0\le 0.1$) and small electron-phonon coupling ($g<1$) where the small parameter is $t/{\omega }_0$. We map our polaronic Hamiltonian onto a next-to-nearest-neighbor interaction anisotropic Heisenberg spin model. By studying the mass gap and the power-law exponent of the spin-spin correlation function for our Heisenberg spin model, we analyze the Luttinger liquid to charge-density-wave transition at half-filling in the effective polaronic Hamiltonian. We calculate the structure factor at all fillings and find that the spin-spin correlation length decreases as one deviates from half-filling. We also extend our derivation of polaronic Hamiltonian to $d$-dimensions.

Content changed. Accepted in Phys. Rev. B

References in corpus (4)

• Phase diagram of the one-dimensional Holstein model of spinless fermions
• Froehlich-Coulomb model of high-temperature superconductivity and charge segregation in the cuprates
• Isotope effect on the electron band structure of doped insulators
• Colossal Magnetoresistance using the Small Polaron Picture with Finite Bandwidth Effects

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• Giant magnetoelectric effect in pure manganite-manganite heterostructures
• Phase transition and phase diagram at a general filling in the spinless one-dimensional Holstein Model
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• Experimental and theoretical demonstration of negative magnetization induced by particle size reduction in nano-form Gd${}_{1-x}$Ca${}_x$MnO${}_3$
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