Product Vacua and Boundary State Models in d Dimensions

Abstract

We introduce and analyze a class of quantum spin models defined on d-dimensional lattices Lambda subset of Z^d, which we call `Product Vacua with Boundary States' (PVBS). We characterize their ground state spaces on arbitrary finite volumes and study the thermodynamic limit. Using the martingale method, we prove that the models have a gapped excitation spectrum on Z^d except for critical values of the parameters. For special values of the parameters we show that the excitation spectrum is gapless. We demonstrate the sensitivity of the spectrum to the existence and orientation of boundaries. This sensitivity can be explained by the presence or absence of edge excitations. In particular, we study a PVBS models on a slanted half-plane and show that it has gapless edge states but a gapped excitation spectrum in the bulk.

References in corpus (7)

• Propagation of Correlations in Quantum Lattice Systems
• Elementary excitations in gapped quantum spin systems
• On topological phases of spin chains
• Edge theories in Projected Entangled Pair State models
• Robustness in Projected Entangled Pair States
• On gapped phases with a continuous symmetry and boundary operators
• Classifying Quantum Phases With The Torus Trick

Cited by in corpus (15)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• An area law for 2D frustration-free spin systems
• Spectral gaps of frustration-free spin systems with boundary
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• A class of two-dimensional AKLT models with a gap
• Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces
• Divide and conquer method for proving gaps of frustration free Hamiltonians
• Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons
• Random translation-invariant Hamiltonians and their spectral gaps
• Gapped PVBS models for all species numbers and dimensions
• Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• Topologically ordered states in infinite quantum spin systems
• Knabe's spectral gap method for open boundary conditions