Bipolaronic charge density waves and polaronic spin density waves in the Holstein-Hubbard model

Abstract

At large electron-phonon coupling, the phonon of the Holstein-Hubbard model can be (generally) treated classically. Exact results can be obtained for this model at any band filling and any finite dimension where the Hubbard term with coefficient U is treated rigorously. The existence of chaotic bipolaronic states is proven when U is smaller than a certain value U c and for an electron-phonon coupling k sufficiently large. The existence of magnetic polaronic states is also proven for positive U and k sufficiently large. For 0<U<U c , there exists an overlap region with chaotic mixed polaronic-bipolaronic states. There is a region for U≃U c /2 and large k of special interest, where the bipolarons in their ground-state become singlet pairs of polarons bounded by a magnetic resonance. Then, the Peierls-Nabarro barrier which usually pins polarons and bipolarons to the lattice depresses to almost zero and the validity of the classical lattice approximation breaks down so that the initial exact results do not apply in that specific region. The formation of a superconducting state with possibly a high critical temperature, is then conjectured at a large coupling k in a narrow domain in-between the two insulating domains corresponding to Bipolaronic Charge Density Waves and to magnetic Polaronic Spin Density Waves respectively