Critical behavior of dirty parafermionic chains

Abstract

A family of ${\mathbb{Z}}_n$-symmetric non-Hermitian models of Baxter was shown by Fendley to be exactly solvable via a parafermionic generalization of the Clifford algebra. We study these models with spatially random couplings, and obtain several exact results on thermodynamic singularities as the distributions of couplings are varied. We find that these singularities, independent of $n$, are identical to those in the random transverse-field Ising chain; correspondingly the models host infinite-randomness critical points. Similarities in structure to exact methods for random Ising models, a strong-disorder renormalization group, and generalizations to other models with free spectra, are discussed.

References in corpus (21)

• Free parafermions
• An Impurity Driven Phase Transition in the Antiferromagnetic Spin-1 Chain
• Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains
• Critical Properties of Random Quantum Potts and Clock Models
• Percolation Transition in the random antiferromagnetic spin-1 chain
• Free fermions in disguise
• Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains
• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains
• Free fermions behind the disguise
• Integrable quantum spin chains with free fermionic and parafermionic spectrum
• Parafermions in the tau-2 model
• Random Antiferromagnetic SU(N) Spin 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
• Anomalous bulk behaviour in the free parafermion $Z(N)$ spin chain
• Random SU(2)-symmetric spin-$S$ chains
• Some ground-state expectation values for the free parafermion Z(N) spin chain
• Superuniversality from disorder at two-dimensional topological phase transitions
• Random free-fermion quantum spin chain with multi-spin interactions