Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2004-08-24
Physics
Condensed Matter
Strongly Correlated Electrons
Content changed. Accepted in Phys. Rev. B
Scientific paper
10.1103/PhysRevB.71.235118
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.
Das Arnab
Datta Sanjoy
Yarlagadda Sudhakar
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