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

TL;DR

This paper introduces a systematic method for constructing lattice models with exactly solvable boundary states of arbitrary codimension, applicable to both topological and non-topological phases, enhancing understanding of boundary phenomena.

Contribution

The authors develop a generic approach to create D-dimensional lattice models with exact boundary states of any codimension, valid under simple locality conditions.

Findings

Models include boundary states at corners, edges, hinges, and surfaces.

Exact solutions are robust across parameter variations within locality constraints.

Framework applies to both topological and non-topological phases.

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.