Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains

Abstract

We introduce a family of SO($n$)-symmetric spin chains which generalize the transverse-field Ising chain for $n=1$. These spin chains are defined with Gamma matrices and can be exactly solved by mapping to $n$ species of itinerant Majorana fermions coupled to a static ${\mathbb{Z}}_2$ gauge field. Their phase diagrams include a critical point described by the $\mathrm{Spin}(n{)}_1$ conformal field theory as well as two distinct gapped phases. We show that one of the gapped phases is a trivial phase and the other realizes a symmetry-protected topological phase when $n\ge 2$. These two gapped phases are proved to be related to each other by a Kramers-Wannier duality. Furthermore, other elegant structures in the transverse-field Ising chain, such as the infinite-dimensional Onsager algebra, also carry over to our models.

12 pages, 3 figures; Eq. (39) has been corrected

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Cited by in corpus (5)

• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Topological physics in quantum critical systems
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Conserved Charges of Series of Solvable Lattice Models
• Transverse Field $\gamma$-Matrix Spin Chains