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4.5. VARIATIONAL MONTE-CARLO APPLIED TO THE CARBON NANOTUBES103
Tube Evar/N EQMC/N MAF φa1
φa2
φa3
|∆ max a1 | |∆ max a2 | |∆ max a3
|
∆S
2D −0.5430(1) −0.5450(10) 0.330(2) 0 0.66(1) 1.33(1) 0.0100(1) 0.0100(1) 0.0100(1) 0
(3,0) −0.5458(1) −0.5498(5) 0.290(2) 1.50(1) 1.00(1) 0.0140(1) 0.0069(1) 0.0140(1) 0.110(10) 0.110(10)
(2,2) −0.5435(1) −0.5482(5) 0.290(2) 1.25(1) 1.00(1) 0.0140(1) 0.0110(1) 0.0140(1) 0.094(5) 0.094(5)
(4,0 −0.5425(1) −0.5468(10) 0.320(2) 0 1.25(1) 0.25(1) 0.0070(1) 0.0080(1) 0.0070(1) 0.04(1)
(2,1) −0.5475(1) −0.5529(1) 0.240(2) 0 1.25(1) 0.75(1) 0.0100(1) 0.0080(1) 0.0080(1) 0.14(1)
(3,1) −0.5426(1) −0.5472(1) 0.330(2) 0 1.50(1) 0.90(1) 0.011(1) 0.013(1) 0.011(1) 0.028(2)
(3,2) −0.5427(1) −0.5462(1) 0.328(2) 0 1.31(1) 0.82(1) 0.005(1) 0.007(1) 0.007(1) 0.026(1)
Table 4.3: Heisenberg energies per site E/N obtained in the variational wavefunction (Evar) andbyQMC(EQMC) are
shown. Both the energy and the staggered magnetization per site MAF were extrapolated to the thermodynamic limit.
) of the pairing observable obtained at optimal doping are shown. The
phases are in units of π. Finally, the spin-gap ∆S obtained by QMC is depicted.
Also the amplitude (|∆ max |) and the phase
ai
(φai