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Related Experiment Video

Updated: Jan 20, 2026

Molecular Entanglement and Electrospinnability of Biopolymers
07:59

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Local entanglement and string order parameter in dimerized models.

Murod S Bahovadinov1, Oğuz Gülseren, Jürgen Schnack

  • 1Department of Physics, Bilkent University, 06800, Bilkent, Ankara, Turkey. Fakultät für Physik, Universität Bielefeld, D-33501 Bielefeld, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|September 6, 2019
PubMed
Summary

We introduce a string order parameter (SOP) to detect symmetry-protected topological phases in fermionic systems. This method reveals a topological quantum phase transition in a dimerized spin chain model.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Topological Phases of Matter

Background:

  • Symmetry-protected topological phases (SPTs) are crucial in understanding exotic quantum states.
  • String order parameters (SOPs) are effective for characterizing topological phases in quantum spin systems.
  • Extending these concepts to fermionic systems is an active area of research.

Purpose of the Study:

  • To propose and validate the application of SOPs for identifying SPTs in fermionic systems.
  • To investigate the topological quantum phase transition (tQPT) in a generalized dimerized model.
  • To explore the utility of local entanglement measures in characterizing tQPTs.

Main Methods:

  • Utilized Jordan-Wigner fermionization to map a spin-1/2 XX model to a spinless Su-Schrieffer-Heeger (SSH) fermionic model.
  • Employed reconstructed SOPs, evaluated as determinants of Toeplitz matrices, to analytically demonstrate phase transitions.
  • Analyzed pairwise concurrence as a local entanglement measure to probe microscopic correlations near tQPT.

Main Results:

  • Successfully demonstrated the identification of a phase transition between trivial and Haldane phases using SOPs in the fermionic model.
  • Showcased the effectiveness of SOPs in characterizing topological phases in fermionic systems.
  • Observed non-analytic behavior in the first derivative of pairwise concurrence at the tQPT, analogous to second-order trivial quantum phase transitions.

Conclusions:

  • String order parameters provide a robust tool for detecting symmetry-protected topological phases in fermionic systems.
  • The study establishes a connection between spin models and fermionic topological phases via Jordan-Wigner transformation.
  • Local entanglement measures like concurrence offer valuable insights into the nature of topological quantum phase transitions.