Probing the Kosterlitz-Thouless transition in 1D Heisenberg antiferromagnet based on topological properties of its ground state

Abstract

A Kosterlitz-Thouless phase transition in the ground state of an antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain with nearest and next-nearest-neighbor interactions is re-investigated from a different perspective: An unequivocal correspondence is found between components of the scalar product $⟨{\Psi }_0|{\Psi }_0⟩$ and geometrical objects. One can classify these objects according to whether any two of them can be transformed into each other in a continuous way (belong to the same homotopy class). A finite size scaling of the "connection term`` $⟨{\Psi }_0|\partial {\Psi }_0⟩$ with respect to chain length (16, 18, 20, 22, 24 spins) for each homotopy class of above mentioned objects leads to the critical value of $\lambda$ with rather high accuracy.

The paper contained some inaccuracies. Completely rewritten and extended is available as arXiv:2103.16203

Cited by in corpus (1)

• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model