Integrable Anyonenketten

• Antragsteller: Professor Dr. Holger Frahm
• Fachliche Zuordnung: Theoretische Physik der kondensierten Materie
• Förderung: Förderung von 2013 bis 2016
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 228344630

• Erstellungsjahr: 2016

Zusammenfassung der Projektergebnisse

Within this project we have constructed several one-dimensional models of interacting non-Abelian anyons (or topological charges) satisfying a given fusion algebra. Employing the face-vertex correspondence to a related spin chain model or by Baxterization of the corresponding braiding relations we have identified choices of the coupling constants where these models are integrable. To solve their spectral problem and identify the effective theory for low energy excitations we have developed functional Bethe ansatz methods which can be used to study integrable models of interacting anyons from more general (including higher rank) fusion algebras.

Projektbezogene Publikationen (Auswahl)

• The D(D3 )-anyon chain: integrable boundary conditions and excitation spectra, New J. Phys. 15 (2013) 053035
  Peter E. Finch and Holger Frahm
  (Siehe online unter https://doi.org/10.1088/1367-2630/15/5/053035)
• Integrable anyon chains: from fusion rules to face models to effective field theories, Nucl. Phys. B 889 (2014) 299-332
  Peter E. Finch, Michael Flohr, and Holger Frahm
  (Siehe online unter https://doi.org/10.1016/j.nuclphysb.2014.10.017)
• Inversion identities for inhomogeneous face models, Nucl. Phys. B 887 (2014) 423-440
  Holger Frahm and Nikos Karaiskos
  (Siehe online unter https://doi.org/10.1016/j.nuclphysb.2014.08.013)
• Quantum phases of a chain of strongly interacting anyons, Phys. Rev. B 90 (2014) 081111(R)
  Peter E. Finch, Holger Frahm, Marius Lewerenz, Ashley Milsted,Tobias J. Osborne
  (Siehe online unter https://doi.org/10.1103/PhysRevB.90.081111)
• Non-Abelian SU (3)k anyons: inversion identities for higher rank face models, J. Phys. A: Math. Theor. 48 (2015) 484001
  Holger Frahm and Nikos Karaiskos