Emergence of Bose Liquid in Cuprates: Low-Energy Effective Theory of the Emery Model

We investigate the low-energy effective theory of the Emery model applicable to cuprates.  In addition to the emergence of non-local many-body coupling, the kinetic processes are found to be strongly dressed.  In the strong interaction regime, diagonalization of local many-body problem indicates multiple emerged mechanisms that promote the formation of tightly bound bosonic carriers.  Particularly, antiferromagnetic coupling between the Cu d-orbitals plays the essential rule in binding two doped holes on an oxygen atom leading to a weakly coupled spin-boson model of emergent bose liquid.  We then discuss the implication of such low-energy theory on the long-range magnetic correlation.