Topologically distinct classes of valence bond solid states with their parent Hamiltonians

Abstract

We introduce a general method to construct one-dimensional translationally invariant valence bond solid states with a built-in Lie group $G$ and derive their matrix product representations. The general strategies to find their parent Hamiltonians are provided so that the valence bond solid states are their unique ground states. For quantum integer spin-$S$ chains, we discuss two topologically distinct classes of valence bond solid states: One consists of two virtual SU(2) spin-$J$ variables in each site and another is formed by using two $SO(2S+1)$ spinors. Among them, a new spin-1 fermionic valence bond solid state, its parent Hamiltonian, and its properties are discussed in detail. Moreover, two types of valence bond solid states with SO(5) symmetry are further generalized and their respective properties are analyzed as well.

11 pages, 5 figures; to be published in Physical Review B

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Cited by in corpus (34)

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• Fermionic theory for quantum antiferromagnets with spin S > 1/2
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• Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
• Qudit quantum computation on matrix product states with global symmetry
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains
• Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains
• New gapped quantum phases for S=1 spin chain with D2h symmetry
• Continuous quantum phase transition between two topologically distinct valence bond solid states associated with the same spin value
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Product vacua with boundary states
• Haldane Topological Orders in Motzkin Spin Chains
• Generalized Toric Codes Coupled to Thermal Baths
• Entanglement in valence-bond-solid states on symmetric graphs
• Critical theory of the topological quantum phase transition in a spin-2 chain
• Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States
• Topological disentangler for the valence-bond-solid chain
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• All spin-1 topological phases in a single spin-2 chain
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• SU(3) quantum critical model emerging from a spin-1 topological phase
• The matrix product representation for the q-VBS state of one-dimensional higher integer spin model
• Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry protected topological phases
• Exact renormalization in quantum spin chains
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Symmetry-protected intermediate trivial phases in quantum spin chains
• Spin-spin correlation functions of the q-VBS state of an integer spin model
• Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters
• Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Reconfigurable dissipative entanglement between many spin ensembles: from robust quantum sensing to many-body state engineering