Topological charge scaling at a quantum phase transition

Authors:

• Piotr Tomczak

Abstract

We reexamine the Kosterlitz-Thouless phase transition in the ground state |Ψ0⟩ of an antiferromagnetic spin-12 Heisenberg chain with nearest- and next-nearest-neighbor interactions λ from a different perspective: After defining winding number (topological charge) W in the basis of resonating valence bond states, the finite-size scaling of ⟨Ψ0|W|Ψ0⟩, ⟨Ψ0|W|∂λΨ0⟩, ⟨∂λΨ0|W|∂λΨ0⟩ leads to the accurate value of critical coupling λc=0.2412±0.0007 and to the value of subleading critical exponent ν=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.