## Abstract

It is well-known that the ground-state of models with electron-phonon coupling, may be either a charge density wave (CDW) or a superconductor (SC). For describing CDWs, standard theories require low dimensional models and consider that the Born-Oppenheimer approximation is valid. Then, in the incommensurate case and with the help of some extra approximations, the existence of strictly gapless phonons called phasons is well admitted. However, some years ago, we predicted on the basis of numerical calculations that CDWs with phason modes with a non-zero gap could exist^{[1,2]}. More recently, we noted that because of a tunnelling energy gain allowed by the quantum lattice fluctuations, phase defect energies of CDWs could become negative below the transition by breaking of analyticity when the phason gap is zero or very small^{[23,4}]. Thus, we suggested a conclusion which is very controversial, that CDWs with a strictly zero phason gap should be always unstable against quantum lattice fluctuations. Although the other part of our talk dealing with the concept of anti-integrability is also relevant for understanding bipolaronic CDWs, the reader is refereed to existing publications^{[5,6]} and in preparation[7]. In this short proceeding, we prefer to discuss the most controversial part of this problem and to present new arguments supporting this conjecture. We first briefly describe the theorem which predicts for large enough electron-phonon coupling, the existence of bipolaronic chaotic states for the Holstein model at any dimension, in the adiabatic limit. The ground-state of this model is thus an ordered insulating bipolaronic structure (CDW) with a strictly non zero phason gap. Early numerical observations in one dimension are thus confirmed and extended^{[1,2]}.

## Keywords

Unitary Transformation Charge Density Wave Adiabatic Limit Holstein Model Charge Density Wave State## Preview

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## References

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