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4.5. VARIATIONAL MONTE-CARLO APPLIED TO THE CARBON NANOTUBES101<br />
Nanotube 〈S i · S i+a1 〉 〈S i · S i+a2 〉 〈S i · S i+a3 〉<br />
(2, 2)<br />
QMC −0.376(1) −0.360(1) −0.360(1)<br />
VMC ∆/AF −0.372(1) −0.360(1) −0.356(1)<br />
VMC ∆ −0.379(1) −0.350(1) −0.349(1)<br />
VMC Gutzwiller −0.316(1) −0.360(1) −0.368(1)<br />
(3, 0)<br />
QMC −0.374(1) −0.354(1) −0.374(1)<br />
VMC ∆/AF −0.369(1) −0.348(1) −0.373(1)<br />
VMC ∆ −0.374(1) −0.336(1) −0.377(1)<br />
VMC Gutzwiller −0.360(1) −0.330(1) −0.362(1)<br />
(4, 0)<br />
QMC −0.367(1) −0.356(1) −0.369(1)<br />
VMC ∆/AF −0.364(1) −0.351(1) −0.370(1)<br />
VMC ∆ −0.372(1) −0.313(1) −0.386(1)<br />
VMC Gutzwiller −0.370(1) −0.310(1) −0.376(1)<br />
(2, 1)<br />
QMC −0.392(1) −0.339(1) −0.373(1)<br />
VMC ∆/AF −0.410(1) −0.330(1) −0.363(1)<br />
VMC ∆ −0.430(1) −0.308(1) −0.353(1)<br />
VMC Gutzwiller −0.434(1) −0.264(1) −0.355(1)<br />
(3, 1)<br />
QMC −0.366(1) −0.359(1) −0.371(1)<br />
VMC ∆/AF −0.363(1) −0.352(1) −0.371(1)<br />
VMC ∆ −0.354(1) −0.312(1) −0.407(1)<br />
VMC Gutzwiller −0.351(1) −0.380(1) −0.322(1)<br />
(3, 2)<br />
QMC −0.369(1) −0.362(1) −0.360(1)<br />
VMC ∆/AF −0.373(1) −0.355(1) −0.362(1)<br />
VMC ∆ −0.390(1) −0.319(1) −0.360(1)<br />
VMC Gutzwiller −0.380(1) −0.313(1) −0.361(1)<br />
Table 4.2: Nearest-neighbor exchange energy in the three directions for a 144 site<br />
clusters for various wavefunctions are depicted. Data obtained with the Quantum<br />
Monte-Carlo method are also shown.
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