Topological charge scaling at a quantum phase transition

We reexamine the Kosterlitz-Thouless phase transition in the ground state vertical bar Psi(0)> of an antiferromagnetic spin-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 <Psi(0)vertical bar W vertical bar Psi(0)>, <Psi(0)vertical bar W vertical bar delta(lambda) Psi(0)>, <delta(lambda) Psi(0)vertical bar W vertical bar delta(lambda) Psi(0)> leads to the accurate value of critical coupling lambda(c) = 0.2412 +/- 0.0007 and to the value of subleading critical exponent nu = 2.000 +/- 0.001. This approach should be useful when examining the topological phase transitions in all systems described in the basis of resonating valence bonds.