We reexamine the Kosterlitz-Thouless phase transition in the ground state $|{\mathrm{\Psi }}_0\rangle$ of an antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain with nearest- and next-nearest-neighbor interactions $\lambda$ from a different perspective: After defining winding number (topological charge) $W$ in the basis of resonating valence bond states, the finite-size scaling of $\langle {\mathrm{\Psi }}_0\left|W\right|{\mathrm{\Psi }}_0\rangle , \langle {\mathrm{\Psi }}_0\left|W\right|{\partial }_{\lambda }{\mathrm{\Psi }}_0\rangle , \langle {\partial }_{\lambda }{\mathrm{\Psi }}_0\left|W\right|{\partial }_{\lambda }{\mathrm{\Psi }}_0\rangle$ leads to the accurate value of critical coupling ${\lambda }_c=0.2412\pm 0.0007$ and to the value of subleading critical exponent $\nu =2.000\pm 0.001$. This approach should be useful when examining the topological phase transitions in all systems described in the basis of resonating valence bonds.

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• Quantum phase transitions
• Topological phase transition
• Scaling methods