Symmetry breaking phases and transitions in an Ising fusion category lattice model
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| Format: | Preprint |
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2026
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| _version_ | 1866914498232713216 |
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| author | Roychowdhury, Soumil Wang, Chenjie |
| author_facet | Roychowdhury, Soumil Wang, Chenjie |
| contents | An anyon-chain-like lattice model with symmetry described by the Ising fusion category is studied. Combining numerical and analytical studies, we uncover a rich phase diagram that contains three phases: a symmetric critical phase and two categorical symmetry breaking phases. The symmetric phase lies in the same universality class as the usual critical Ising model. The first symmetry-breaking phase, dubbed the \emph{categorical ferromagnetic} phase, has the Ising fusion category fully broken and exhibits a threefold ground-state degeneracy, as expected from the generalized Landau paradigm. The other symmetry-breaking phase is analogous to a conventional antiferromagnet: it breaks lattice translation and part of the Ising fusion category, and therefore is termed the \emph{categorical antiferromagnetic} phase. Unlike ordinary antiferromagnetic states associated with finite invertible symmetry breaking, this phase itself is critical, being described by a fourfold degenerate Ising conformal field theory. We argue more generally that antiferromagnetic states associated with broken non-invertible symmetries have a large low-energy manifold that grows exponentially in system size, due to the greater-than-one quantum dimension of domain walls. We also numerically study the transitions between the three phases. The transition between the symmetric and categorical ferromagnetic phase is described by the $c=7/10$ tricritical Ising CFT, while the transition between the symmetric and categorical antiferromagnetic phases is less understood. Our numerical data suggest that the latter transition is continuous and described by a conformal field theory with central charge $c=3/2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry breaking phases and transitions in an Ising fusion category lattice model Roychowdhury, Soumil Wang, Chenjie Strongly Correlated Electrons High Energy Physics - Theory An anyon-chain-like lattice model with symmetry described by the Ising fusion category is studied. Combining numerical and analytical studies, we uncover a rich phase diagram that contains three phases: a symmetric critical phase and two categorical symmetry breaking phases. The symmetric phase lies in the same universality class as the usual critical Ising model. The first symmetry-breaking phase, dubbed the \emph{categorical ferromagnetic} phase, has the Ising fusion category fully broken and exhibits a threefold ground-state degeneracy, as expected from the generalized Landau paradigm. The other symmetry-breaking phase is analogous to a conventional antiferromagnet: it breaks lattice translation and part of the Ising fusion category, and therefore is termed the \emph{categorical antiferromagnetic} phase. Unlike ordinary antiferromagnetic states associated with finite invertible symmetry breaking, this phase itself is critical, being described by a fourfold degenerate Ising conformal field theory. We argue more generally that antiferromagnetic states associated with broken non-invertible symmetries have a large low-energy manifold that grows exponentially in system size, due to the greater-than-one quantum dimension of domain walls. We also numerically study the transitions between the three phases. The transition between the symmetric and categorical ferromagnetic phase is described by the $c=7/10$ tricritical Ising CFT, while the transition between the symmetric and categorical antiferromagnetic phases is less understood. Our numerical data suggest that the latter transition is continuous and described by a conformal field theory with central charge $c=3/2$. |
| title | Symmetry breaking phases and transitions in an Ising fusion category lattice model |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.20201 |