- E. Altman and A. Auerbach,
Phys. Rev. B
**65**, 104508 (2002).

Accueil du site > Divers > Sylvain Capponi > Highlights on Global Phase Diagram

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- 16 février 2006

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.

- E. Altman and A. Auerbach,
Phys. Rev. B
**65**, 104508 (2002).