Product vacua with boundary states

Abstract

We introduce a family of quantum spin chains with nearest-neighbor interactions that can serve to clarify and refine the classification of gapped quantum phases of such systems. The gapped ground states of these models can be described as a product vacuum with a finite number of particles bound to the edges. The numbers of particles, n_L and n_R, that can bind to the left and right edges of the finite chains serve as indices of the particular phase a model belongs to. All these ground states, which we call Product Vacua with Boundary States (PVBS) can be described as Matrix Product States (MPS). We present a curve of gapped Hamiltonians connecting the AKLT model to its representative PVBS model, which has indices n_L=n_R=1. We also present examples with n_L=n_R=J, for any integer J\geq 1, that are related to a recently introduced class of SO(2J+1)-invariant quantum spin chains.

New section on SO(2J+1)-invariant models

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Cited by in corpus (16)

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• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
• On gapped phases with a continuous symmetry and boundary operators
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
• Product Vacua and Boundary State Models in d Dimensions
• Product vacua with boundary states and the classification of gapped phases
• Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces
• $C^1$-classification of gapped parent Hamiltonians of quantum spin chains
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III
• Connected components of irreducible maps and 1D quantum phases
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins
• Projected Entangled Pair States with continuous virtual symmetries
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• Gapped and gapless phases of frustration-free spin-1/2 chains
• On ground state phases of quantum spin systems