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\begin{document}
\title{Kosterlitz--Thouless transition  in 1D Heisenberg antiferromagnet: An evidence  based on topological properties of the ground state}
\author{\underline{Piotr Tomczak}}
\affiliation{Faculty of Physics, Adam Mickiewica University,  Umultowska 85, 61-614 Poznań, Poland}
\author{Piotr Jabłoński}
\affiliation{Faculty of Physics, Adam Mickiewica University,  Umultowska 85, 61-614 Poznań, Poland}
\begin{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 new perspective: A mapping of the components of the scalar product onto a set of loops is found. One
can classify these loops according to whether any two 
of them can be transformed into each other in a continuous way (i.e., whether they have the same winding number).
A finite size scaling of the fidelity susceptibility and geometrical phase calculated
 within each class of above mentioned loops 
leads to the accurate critical coupling constant value and enables one to find that the critical exponent $\nu=2.000\pm0.001$.


\end{abstract}
\maketitle

\end{document}
