Optical phonons in a quarter-filled one-dimensional Hubbard model

Abstract

The influence of dispersion-less quantum optical phonons on the phase diagram of a quarter-filled Hubbard chain is studied using the Density-matrix renormalization group technique. The ground state phase diagram is obtained for frequencies corresponding to the intramolecular vibrations in organic conductors. For high vibrational modes the system is only slightly affected by the electron-phonons coupling. It remains in a Lüttinger liquid phase as long as the electronic repulsion is larger than the polaronic binding energy. For low vibrational modes the phase diagram is very rich. A noticeable point is the existence of a 4kF CDW phase for small values of the correlation strength. For realistic values of the electron repulsion and of the electron-phonons coupling constant a large phonons-mediated reduction of the Lüttinger liquid parameter Kρ was found compared to the pure electronic model.

Fractionally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

“…As already mentioned by different authors 16,19 , on-site 4k F CDW have the property to allow simultaneaous 2k F SDW. Although the metal-insulator instability in (TMTTF) 2 X (X=PF 6 , AsF 6 , etc...) is believed to be of the Mott-Hubbard type, the recent experiments 6-8 revealing, at lower temperatures, a 4k F charge modulation on the (TMTTF) molecules suggest that relaxation of the molecules (together with the coupling to the anions) might play a dominant role.…”

“…On the contrary, in the uniform phase, strictly speaking A ≃ 0 and the charge correlation function decays as a power law. It has been argued that, although phononic quantum fluctuations are present, such state still belongs to the Luttinger Liquid universality class 14,16 . In that case, the extra Q = + e 2 charge is totally spread over the full chain.…”

“…In order to render the calculations feasible, the basis set has been truncated on each site to the two lowest vibronic states. This choice is physically reasonable as long as the frequency ω is not too small since only the lowest vibronic states are expected to be involved 16 . In all cases, we kept m = 216 states per renormalized block.…”

“…This instability is in fact enhanced by the lattice (ω = 0) coupling and the 4k F CDW phase becomes stable even when V < 2 (and J finite) for K −1 exceeding a V -dependant critical value 12 . The numerical study of the model with quantum phonons using the infinite system DMRG method 13 requires an approximate (but reliable) treatment of the phonon degrees of freedom [14][15][16] . Indeed, an infinite number of phononic quantum states lives on each site.…”

Density Matrix Renormalization

“…The phase diagram for the nondisordered Bose-Hubbard model, showing a reentrance of the superfluid phase into the insulating phase, was calculated in [212]. It has also been used to study a chain of oscillators with optical phonon spectrum [213] and optical phonons in the quarter-filled Hubbard model for organic conductors [214].…”