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 ${\nu }_{\perp }=2/N$.

arXiv comment8 pages, 1 figure, minor changes, connection to hypergeometric function

References in corpus (7)

• Topological phases with parafermions: theory and blueprints
• Free parafermions
• Transfer matrix functional relations for the generalized tau_2(t_q) model
• Critical Exponents of the Chiral Potts Model from Conformal Field Theory
• Parafermions in the tau-2 model
• Reflection Positivity for Parafermions
• The ${\tau }_2$ model and parafermions

Cited by in corpus (13)

• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Integrable quantum spin chains with free fermionic and parafermionic spectrum
• General phase spaces: from discrete variables to rotor and continuum limits
• Superintegrability of Geodesic Motion on the Sausage Model
• Quantum Ising chain with boundary dephasing
• Free-parafermionic $Z(N)$ and free-fermionic $XY$ quantum chains
• Exceptional Points in the Baxter-Fendley Free Parafermion Model
• Anomalous bulk behaviour in the free parafermion $Z(N)$ spin chain
• 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
• Critical behavior of dirty parafermionic chains
• Noninteracting tight-binding models for Fock parafermions