Hidden charge 2e boson in doped Mott insulators

We construct the low energy theory of a doped Mott insulator, such as the high-temperature superconductors, by explicitly integrating over the degrees of freedom far away from the chemical potential. For either hole or electron doping, integration of the high energy scale generates a charge 2e bosonic field that accounts for dynamical spectral weight transfer across the Mott gap. The bosonic field represents non-projective physics as its vanishing leads to the standard projected result, namely the $t-J$ model. A mean-field solution reveals that the free energy acquires a lower value in the presence of the bosonic field than when it is absent. Moreover, we find that at mean-field boson condensation defeats d-wave superconducting order in the vicinity of half-filling. The relationship between boson condensation and local-pairing in the pseudogap phase of the cuprates is explored.