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arXiv · 2305.03398

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

Sreejith Chulliparambil·Hua-Chen Zhang·Hong-Hao Tu
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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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Sreejith Chulliparambil, Hua-Chen Zhang, Hong-Hao Tu. 2023-05-05. Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains. https://doi.org/10.1103/physrevb.108.094411

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