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Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions

Pavel Bleher

New Trends in Mathematical PhysicsJan 1, 200931 citations

Classification of gapped domain walls of topological orders in 2+1 dimensions: a Levin-Wen model realization

Y. F. Chen, Siyuan Wang, Yu Zhao +2 more

A bstract This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].A bstract This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].

arXiv:2502.07664Journal of High Energy PhysicsJun 11, 20251 citation

A Remark on Gapped Domain Walls Between Topological Phases

Yasuyuki Kawahigashi

arXiv:1504.01088Letters in Mathematical PhysicsMay 26, 201520 citations

Edge pinning and internal phase transitions in a system of domain walls

Theodore W. Burkhardt, P. Schlottmann

The European Physical Journal BJun 1, 19852 citations

2 Models for gapped boundaries and domain walls

Alexei Kitaev, Liang Kong

We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category $\calC$ as in the Levin-Wen model, whereas the boundary is associated with a module category over $\calC$. We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category $\calC$ as in the Levin-Wen model, whereas the boundary is associated with a module category over $\calC$. We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.

Aug 17, 2016431 citations

The border model in one dimension

George Allen Baker Jr., James D. Johnson

Journal of Statistical PhysicsFeb 1, 19900 citations

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