A two-parameter S3-invariant spin chain has four gapped phases, including a new 'not-A' phase and a representation symmetry-protected topological phase, with all transitions in the three-state Potts universality class.
Self-dual $S_3$-invariant quantum chains
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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.
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cond-mat.stat-mech 1years
2019 1verdicts
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The "not-A", RSPT and Potts phases in an $S_3$-invariant chain
A two-parameter S3-invariant spin chain has four gapped phases, including a new 'not-A' phase and a representation symmetry-protected topological phase, with all transitions in the three-state Potts universality class.