Topological charge scaling at a quantum phase transition

Abstract

We reexamine the Kosterlitz-Thouless phase transition in the ground state $|{\Psi }_0⟩$ 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 $⟨{\Psi }_0|W|{\Psi }_0⟩$, $⟨{\Psi }_0|W|{\partial }_{\lambda }{\Psi }_0⟩$, $⟨{\partial }_{\lambda }{\Psi }_0|W|{\partial }_{\lambda }{\Psi }_0⟩$ 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.

arXiv comment5 pages, 4 figures

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