"Not-A", representation symmetry-protected topological, and Potts phases in an S-3-invariant chain

Journal article

We analyze in depth an S 3 -invariant nearest-neighbor quantum chain in the region of a U ( 1 ) -invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has “representation” symmetry-protected topological (RSPT) order, while its dual exhibits an unusual “not- A ” order, where the spins prefer to align in two of the three directions. Within each of the four phases, we find a frustration-free point with exact ground state(s). The exact ground states in the not- A phase are product states, each an equal-amplitude sum over all states where one of the three spin states on each site is absent. Their dual, the RSPT ground state, is a matrix product state similar to that of Affleck-Kennedy-Lieb-Tasaki. A field-theory analysis shows that all transition lines are in the universality class of the critical three-state Potts model. They provide a lattice realization of a flow from a free-boson field theory to the Potts conformal field theory.

Authors: O'Brien, E; Vernier, E; Fendley, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review B
• Volume: 101
• Issue: 23
• Article number: 235108
• Publication date: 2020-06-01
• Acceptance date: 2020-05-14
• DOI: 10.1103/PhysRevB.101.235108
• EISSN: 2469-9969
• ISSN: 2469-9950
• Language: English
• Keywords: FFR