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arXiv · 1509.07571

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

P. Tomczak·P. Jablonski·M. Tomczak
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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 $\langle \Psi_0| \Psi_0 \rangle$ 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`` $\langle \Psi_0|\partial \Psi_0 \rangle$ 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 $\lambda$ with rather high accuracy.

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P. Tomczak, P. Jablonski, M. Tomczak. 2015-09-25. Probing the Kosterlitz-Thouless transition in 1D Heisenberg antiferromagnet based on topological properties of its ground state. https://arxiv.org/abs/1509.07571

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