Field theory of symmetry-protected valence bond solid states in (2+1) dimensions

Abstract

This paper describes a semiclassical field-theory approach to the topological properties of spatially featureless Affleck-Kennedy-Lieb-Tasaki type valence bond solid ground states of antiferromagnets in spatial dimensions one to three. Using nonlinear sigma models set in the appropriate target manifold and augmented with topological terms, we argue that the path integral representation of the ground-state wave functional can correctly distinguish symmetry-protected topological ground states from topologically trivial ones. The symmetry-protection feature is demonstrated explicitly in terms of a dual field theory, where we take into account the nontrivial spatial structure of topological excitations, which are caused by competition among the relevant ordering tendencies. A temporal surface contribution to the action originating from the bulk topological term plays a central role in our study. We discuss how the same term governs the behavior of the so-called strange correlator. In particular, we find that the path integral expression for the strange correlator in two dimensions reduces to the well-known Haldane expression for the two point spin correlator of antiferromagnetic spin chains.

20 pages, 5 figures

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Cited by in corpus (7)

• Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to Néel Order
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet