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3.4. RESULTS AND DISCUSSION 77
0
0
-0.2
-0.4
e pot
e kinetic
-0.4
-0.8
0 0.4 0.8
Hole doping δ
0 0.4 0.8
Hole doping δ
Figure 3.17: Kinetic (e kinetic ) and exchange energy (e pot ) per site for the
Gutzwiller (bold line), the commensurate flux phase with 2π/3 flux per plaquette
(open circles), with π/2 flux per plaquette (dashed line), the d + /AF/J
wavefunctions (filled squares), and the polarized wavefunctions (lines) with
S z =11, 18, 21, 24, 28. The polarized wavefunction are shown from top to bottom
with increasing (decreasing) polarizations in the left (right) figure. the left figure
and decreasing polarization.
tivity and the spin-density wave was found: the energy is minimized either for
(∆ k =0,f(Q) ≠0),or(∆ k ≠0,f(Q) = 0) depending on the doping, with ∆ k of
d x 2 −y 2 + id xy symmetry type in the latter case. Measuring the on-site magnetization
value, we found that the spin-density wave forms a collinear stripe-like
pattern in the spin degrees of freedom, whereas the charge is found to be uniformly
distributed among the lattice sites, as expected (see Fig. 3.16). The amplitude
of the on-site magnetization is shown in Fig. 3.15 as a function of doping.
3.4.4 Phase diagram of the model
Based on our wavefunction we can now give the phase diagram for the doped
system on the triangular lattice. The phase diagram, summarizing the various