Entanglement in the F-AF zig-zag Heisenberg chain

TL;DR

This study investigates the entanglement properties of the F-AF zig-zag Heisenberg chain using DMRG, revealing quantum phase transitions and a potential new phase through concurrence analysis.

Contribution

It demonstrates that concurrence can effectively signal phase transitions and identify complex spin ordering in the F-AF zig-zag Heisenberg chain.

Findings

Concurrence signals quantum phase transitions.

Identifies a new phase with complex spin ordering.

Maps transition lines in the phase diagram.

Abstract

We present a study of the entanglement properties of the F-AF zig-zag Heisenberg chain done by means of the Density Matrix Renormalization Group method. In particular, we have selected the concurrence as measure of entanglement and checked its capability to signal the presence of quantum phase transitions within the previously found ergodicity phase diagram [E. Plekhanov, A. Avella, and F. Mancini, Phys. Rev. B \textbf{74}, 115120 (2006)]. By analyzing the behavior of the concurrence, we have been able not only to determine the position of the transition lines within the phase diagram of the system, but also to identify a well defined region in the parameter space of the model that shows a complex spin ordering indicating the presence of a new phase of the system.