Self-dual $S_3$-invariant quantum chains

Abstract

We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and $S_3$, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct "Fermi velocities". The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.

arXiv comment12+5 pages. v2: presentation changed, results unchanged. v3: minor changes

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• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Phase diagram of the ${\mathbb{Z}}_3$-Fock parafermion chain with pair hopping
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d