Product vacua with boundary states and the classification of gapped phases

Abstract

We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique gapped ground state in the thermodynamic limit that is a simple product state but which on the left and right half-infinite chains, have additional zero energy edge states. The models, which we call Product Vacua with Boundary States (PVBS), form phases that depend only on two integers corresponding to the number of edge states at each boundary. They can serve as representatives of equivalence classes of such gapped ground states phases and we show how the AKLT model and its $SO(2J+1)$-invariant generalizations fit into this classification.

References in corpus (4)

• Bulk-edge correspondence for two-dimensional topological insulators
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Product vacua with boundary states

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• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
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• Gapped PVBS models for all species numbers and dimensions
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