LAUSR

We reexamine the Kosterlitz-Thouless phase transition in the ground state $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}$ of an antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain with nearest- and next-nearest-neighbor interactions $\ensuremath{\lambda}$ from a different perspective: After defining winding number (topological charge) $W$ in the basis of resonating valence bond states, the finite-size scaling of $\ensuremath{\langle}{\mathrm{\ensuremath{\Psi}}}_{0}|W|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}, \ensuremath{\langle}{\mathrm{\ensuremath{\Psi}}}_{0}|W|{\ensuremath{\partial}}_{\ensuremath{\lambda}}{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}, \ensuremath{\langle}{\ensuremath{\partial}}_{\ensuremath{\lambda}}{\mathrm{\ensuremath{\Psi}}}_{0}|W|{\ensuremath{\partial}}_{\ensuremath{\lambda}}{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}$ leads to the accurate value of critical coupling ${\ensuremath{\lambda}}_{c}=0.2412\ifmmode\pm\else\textpm\fi{}0.0007$ and to the value of subleading critical exponent $\ensuremath{\nu}=2.000\ifmmode\pm\else\textpm\fi{}0.001$. This approach should be useful when examining the topological phase transitions in all systems described in the basis of resonating valence bonds.