Integrable anyon chains

• Applicant: Professor Dr. Holger Frahm
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2013 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 228344630

• Final Report Year: 2016

Final Report Abstract

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.

Publications

• The D(D3 )-anyon chain: integrable boundary conditions and excitation spectra, New J. Phys. 15 (2013) 053035
  Peter E. Finch and Holger Frahm
  (See online at 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
  (See online at 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
  (See online at 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
  (See online at 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