Laboratoire de Physique Théorique
Toulouse - UMR 5152

The existence of the preformed hole-pairs in the pseudogap state of underdoped high Tc cuprates bears a strong message, namely, the Cooper pairing between the charge carriers is determined by the dominant energy in the problem. On the length scale that is larger than the Cooper pair size, the long range Coulomb interaction tends to suppress the pair density fluctutations or the long-range phase coherence between pairs. This motivates us to propose a bosonic effective quantum Hamiltonian based on the projected SO(5) model with extended interactions, which can be derived from the microscopic models of the cuprates[1]. The global phase diagram of this model is obtained using mean-field theory and the Quantum Monte Carlo simulation, which is possible because of the absence of the minus sign problem. We show that this single quantum model can account for most salient features observed in the high Tc cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. Experimental consequences are discussed and new theoretical predictions are presented.

FIG.1 : A typical global phase diagram of the cuprates in the parameter space of chemical potential and the ratio of boson hopping energy over interaction energy. This phase diagram shows self-similarity among the insulating PC states at half-filling and other rational filling fractions. There are two types of superfluid-insulator transition. The quantum phase transition of "class A" can be approached by varying the hopping energy, for example, by applying a pressure and magnetic field at constant doping. The quantum phase transition of "class B" can be realized by changing the chemical potential or doping. Different families of cuprates correspond to different traces of "class B". For example, we believe YBCO is B1-like, BSCO may be close to B2-like and LSCO is B3-like. The vertical dash-dot line denotes a boundary in the overdoped region beyond which our pure bosonic model becomes less accurate.

FIG.2 : The global phase diagrams obtained by mean-field calculation(Left panel) and quantum Monte Carlo simulations(Right panel). Here, SC means superconductor, AF means antiferromagnetism and PDW means pair-density-wave. d is the real doping.Dc is the chemical potential and Jc is the hopping energy. The lines are guides to the eyes only.