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124 CHAPTER 5. THE FLUX PHASE FOR THE CUPRATES
Table 5.2: Order parameters for the different wave-functions for V 0 =1.5 and
l 0 = 4. We depict the following order parameters: t i,j × e iφ i,j
,wheret i,j (φ i,j )
is the amplitude (phase) of 〈c + i c j〉, and the exchange energy 〈S i .S j 〉,forthe6
independent bonds labelled for convenience according to Fig. 5.2. The sign of
φ i,j is according to the staggered flux pattern (see arrows in Fig. 5.10). We note
that the RV B/J is uniform by construction. The variational superconducting
order parameter is ∆ RV B =0.3 fortheRV B/J wave-function and ∆ RV B =0
for the SFP/J and BO/J wave-functions.
bond 1 bond 2 bond 3 bond 4 bond 5 bond 6
t i,j
RV B/J 0.077(1) 0.077(1) 0.077(1) 0.077(1) 0.077(1) 0.077(1)
SFP/J 0.085(1) 0.085(1) 0.085(1) 0.085(1) 0.085(1) 0.085(1)
BO/J 0.082(1) 0.083(1) 0.093(1) 0.088(1) 0.086(1) 0.084(1)
|φ i,j |
RV B/J 0 0 0 0 0 0
SFP/J 0.438(1) 0.438(1) 0.438(1) 0.438(1) 0.438(1) 0.438(1)
BO/J 0.527(1) 0.502(1) 0.473(1) 0.390(1) 0.338(1) 0.384(1)
−〈S i .S j 〉
RV B/J 0.215(1) 0.215(1) 0.215(1) 0.215(1) 0.215(1) 0.215(1)
SFP/J 0.197(1) 0.197(1) 0.197(1) 0.197(1) 0.197(1) 0.197(1)
BO/J 0.215(1) 0.207(1) 0.215(1) 0.187(1) 0.186(1) 0.170(1)