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arXiv · 1908.02767

The "not-A", RSPT and Potts phases in an $S_3$-invariant chain

Edward O'Brien·Eric Vernier·Paul Fendley
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Abstract

We analyse 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. Also nearby is a phase with "representation" symmetry-protected topological (RSPT) order. 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 RSPT ground state is similar to that of Affleck-Kennedy-Lieb-Tasaki, whereas its dual 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. A field-theory analysis shows that all transitions 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.

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Edward O'Brien, Eric Vernier, Paul Fendley. 2019-08-07. The "not-A", RSPT and Potts phases in an $S_3$-invariant chain. https://doi.org/10.1103/physrevb.101.235108

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