Parafermions in the tau-2 model

Abstract

It has been shown recently by Baxter that the ${\tau }_2(t_q)$ model with open boundary conditions can be solved by the "parafermionic" method of Fendley. In Baxter's paper there are several conjectures, which were formulated based on numerical short-chain calculations. Here we present the proof of two of them.

21 pages, 1figure; uses iopart.cls with the iopams, amssymb and graphicx packages; also uses overunderset.sty (provided). vs 2: Explanations added and errors corrected, vs 3: More explanations added including Appendix B, vs 4: Expanded Appendix B, vs 5: Reference and links added

References in corpus (2)

• Free parafermions
• The ${\tau }_2$ model and parafermions

Cited by in corpus (15)

• Free fermions in disguise
• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Record statistics for random walks and Lévy flights with resetting
• Integrable quantum spin chains with free fermionic and parafermionic spectrum
• Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires
• Reflection Positivity for Parafermions
• Free-parafermionic $Z(N)$ and free-fermionic $XY$ quantum chains
• The ${\tau }_2$ model and parafermions
• Energy spectrum and critical exponents of the free parafermion $Z_N$ spin chain
• Exceptional Points in the Baxter-Fendley Free Parafermion Model
• Some ground-state expectation values for the free parafermion Z(N) spin chain
• A Brief History of Free Parafermions
• A Graph-Theoretic Framework for Free-Parafermion Solvability
• An exact local mapping from clock-spins to fermions
• Critical behavior of dirty parafermionic chains