Models for Gapped Boundaries and Domain Walls

By Alexei Y. Kitaev, Liang Kong. 2011

483 citations recorded by the source corpus.

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 $${\mathcal C}$$ as in the Levin-Wen model, whereas the boundary is associated with a module category over $${\mathcal C}$$ . 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.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e0ef182173ce71f6d9ab1648289f219e780d84e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, methodology): “The gapped boundary/interface criteria studied by Haldane [77], Kapustin-Saulina [62], Kitaev-Kong [63], LanWang-Wen [64, 68] and many others can be viewed as gauge symmetry-breaking [64–66, 68] or the Anderson-Higgs effect.”
Quantum memories at finite temperature (2014, unknown): “(Barkeshli et al., 2014; Kitaev and Kong, 2012).”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “…gappable, a fact that is known to follow from the feature that the bulk theory of these systems always yields a Lagrangian subgroup of the anyons (Kitaev and Kong, 2012; Levin, 2013): the set of anyons in the bulk can be divided into two sets, one in which every anyon has trivial statistics with…”
Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, background): “KitaevKong [35] extended this Hamiltonian to surfaces with boundary by having the boundary strings take labels inM.”
Bicategories for Boundary Conditions and for Surface Defects in 3-d TFT (2012, methodology): “ that in this case the bicategory of C1-C2 surface defects can be identiﬁed with the bicategory of A1-A2-bimodules. Thus in the special case of TFTs of Turaev-Viro type our results reproduce those of [KK]. Let us explore some consequences of our results. First we consider the special case that the s”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “In particular, it naturally has a dislocation defect which permutes the e and m anyons that encircles the defect [153].”