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

• URL: http://arxiv.org/abs/2305.03398v3
• Date: Sun, 10 Nov 2024 22:06:30 GMT
• Title: Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Authors: Sreejith Chulliparambil, Hua-Chen Zhang, Hong-Hao Tu,
• Abstract summary: We introduce a family of SO($n$)-symmetric spin chains which generalize the transverse-field Ising chain for $n=1$. Their phase diagrams include a critical point described by the $mathrmSpin(n)_1$ conformal field theory.
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• 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 $n \geq 2$. 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.

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