Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension

Abstract

We present a generic and systematic approach for constructing D-dimensional lattice models with exactly solvable d-dimensional boundary states localized to corners, edges, hinges and surfaces. These solvable models represent a class of "sweet spots" in the space of possible tight-binding models---the exact solutions remain valid for any tight-binding parameters as long as they obey simple locality conditions that are manifest in the underlying lattice structure. Consequently, our models capture the physics of both (higher-order) topological and non-topological phases as well as the transitions between them in a particularly illuminating and transparent manner.

arXiv comment19 pages, 12 figures

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• Non-Hermitian systems and topology: A transfer-matrix perspective
• Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Corner modes of the breathing kagome lattice: origin and robustness
• Robustness of topological corner modes against disorder and application to acoustic networks
• Extended Bloch theorem for topological lattice models with open boundaries
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• Dissipative Boundary State Preparation
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• Topological properties of a non-Hermitian quasi-1D chain with a flat band
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• Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators