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Updated: Oct 9, 2025

From Molecules to Materials: Engineering New Ionic Liquid Crystals Through Halogen Bonding
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Free-parafermionic Z(N) and free-fermionic XY quantum chains.

Francisco C Alcaraz1, Rodrigo A Pimenta2

  • 1Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São Carlos, SP, Brazil.

Physical Review. E
|December 24, 2021
PubMed
Summary
This summary is machine-generated.

This study connects Z(N) parafermionic models to novel N-multispin XY quantum chains. The eigenspectra of these XY models encompass all energies from Z(N) parafermionic models via characteristic polynomials.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • The eigenspectra of Ising and XY quantum chains are well-understood, both described by free-fermionic quasiparticles via the Jordan-Wigner transformation.
  • Existing literature features Z(N) quantum chains (N>2) with eigenspectra described by free parafermions, not derived from the standard Jordan-Wigner transformation.

Purpose of the Study:

  • To introduce a new family of XY quantum models incorporating N-multispin interactions.
  • To demonstrate that the eigenspectra of these novel XY models can be expressed using Z(N) free-parafermionic quasienergies.

Main Methods:

  • Introduction of XY models with N-multispin interactions, maintaining U(1) symmetry.
  • Application of the Jordan-Wigner transformation to solve these extended XY models.
  • Establishment of spectral correspondence through the identification of characteristic polynomials.

Main Results:

  • The eigenspectra of the newly introduced N-multispin XY models are shown to be combinations of Z(N) free-parafermionic quasienergies.
  • All eigenenergies of Z(N) free-parafermionic models are found to be present within the eigenspectra of the related free-fermionic XY models.
  • A key difference is noted: Z(N) parafermionic models exhibit an exclusion circle principle absent in the N-multispin XY models.

Conclusions:

  • A direct link is established between N-multispin XY quantum chains and Z(N) free-parafermionic models.
  • The characteristic polynomial serves as the crucial tool for unifying the spectral properties of these distinct quantum systems.
  • This work expands the understanding of solvable quantum models and their spectral relationships.