Abstract
The interplay of strong local electron-lattice and electron-electron interaction is analyzed in the two-dimensional Hubbard-Holstein model using an effective single band Hamiltonian. The effect of the strain field acting on the CuO2 plane and the local cooperative pseudo Jahn Teller vibronic electron-lattice coupling appropriate to cuprate superconductors at optimum doping (i.e.; at doping larger than 1/8) are included via the effective next near neighbor electronic hopping integral t′ (determined by the strain field) close to the local vibronic frequency ω0 (involved in the pseudo Jahn Teller electron lattice coupling). The system shows a characteristic feature of the physics of complex systems, the competition and fluctuation between two states: 1) a first phase of charges self trapped in domains with local lattice distortions (a generalization to a many polaron system of the idea of single intermediate polaron) and 2) a second phase of free carriers.
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