A Brief History of Free Parafermions

Abstract

In this article we outline the historical development and key results obtained to date for free parafermionic spin chains. The concept of free parafermions provides a natural N-state generalization of free fermions, which have long underpinned the exact solution and application of widely studied quantum spin chains and their classical counterparts. In particular, we discuss the Baxter-Fendley free parafermionic Z(N) spin chain, which is a relatively simple non-Hermitian generalization of the Ising model.

13 pages, 2 figures, to appear AAPPS Bulletin

References in corpus (11)

• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Criticality in Translation-Invariant Parafermion Chains
• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Free fermions behind the disguise
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• Reflection Positivity for Parafermions
• Free-parafermionic $Z(N)$ and free-fermionic $XY$ quantum chains
• Energy spectrum and critical exponents of the free parafermion $Z_N$ spin chain
• Ising analogues of quantum spin chains with multispin interactions
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• Confluences of exceptional points and a systematic classification of quantum catastrophes

Cited by in corpus (5)

• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• A Graph-Theoretic Framework for Free-Parafermion Solvability
• Exceptional point rings and $PT$-symmetry in the non-Hermitian XY model
• Noninteracting tight-binding models for Fock parafermions
• Parafermionic representation of Potts-based cluster chain