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The bipolaronic superconducting glass state in the random infinite-range interaction Hubbard model

The phase diagram of the extended Hubbard model with on-site attraction and random inter-site Coulomb energies is studied for the half-filled band case. In the strong coupling limit the problem is mapped onto the system of hard-core bosons (bipolarons) on a lattice, described by the anisotropic pseudo-spin model with infinite-range random exchange interactions-in close analogy to the Sherrington-Kirkpatrick spin-glass approach. It is found that the disorder and frustration strongly affect properties of the system leading to the appearance of the bipolaronic superconducting phase, the bipolaronic superconducting glass state as well as the bipolaronic charge glass phase, depending on the temperature range and the degree of the disorder.