Energy spectrum and critical exponents of the free parafermion $Z_N$ spin chain

Abstract

Results are given for the ground state energy and excitation spectrum of a simple $N$-state $Z_N$ spin chain described by free parafermions. The model is non-Hermitian for $N\ge 3$ with a real ground state energy and a complex excitation spectrum. Although having a simpler Hamiltonian than the superintegrable chiral Potts model, the model is seen to share some properties with it, e.g., the specific heat exponent $\alpha =1-2/N$ and the anisotropic correlation length exponents ${\nu }_{\parallel }=1$ and ${\nu }_{\perp }=2/N$.

8 pages, 1 figure, minor changes, connection to hypergeometric function

References in corpus (1)

• Reflection Positivity for Parafermions

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• Exceptional Points in the Baxter-Fendley Free Parafermion Model
• A Brief History of Free Parafermions
• A Graph-Theoretic Framework for Free-Parafermion Solvability
• Noninteracting tight-binding models for Fock parafermions
• Critical behavior of dirty parafermionic chains