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

TL;DR

This paper investigates the Kosterlitz-Thouless transition in a 1D Heisenberg antiferromagnet by analyzing topological properties of its ground state, revealing a correspondence between scalar products and geometrical objects.

Contribution

It introduces a novel topological approach to identify the phase transition by classifying geometrical objects associated with the ground state wavefunction.

Findings

Identifies a correspondence between scalar product components and geometrical objects.

Finite size scaling yields a precise critical value of the interaction parameter.

Topological classification effectively detects the phase transition.

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.