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arXiv:1509.07571

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

Tomczak, P., Jablonski, P., M. Tomczak

Published Sep 25, 2015• 1 citation
arXivHTMLPDF

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 $\langle Ψ_0| Ψ_0 \rangle$ 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`` $\langle Ψ_0|\partial Ψ_0 \rangle$ 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 $λ$ with rather high accuracy.

DOI
10.48550/arxiv.1509.07571

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