Valence bond solid states with symplectic symmetry

Abstract

We introduce a one-dimensional valence bond solid (VBS) state with symplectic symmetry SP(n) and construct the corresponding parent Hamiltonian. We argue that there is a gap in the spectrum. We calculate exactly the static correlation functions, which fall off exponentially. Hence the model introduced here shares all properties of the Haldane scenario for integer-spin quantum antiferromagnets. We further show that the VBS state possesses string order and discuss its generalization to higher dimensions.

10 pages, 5 figures

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Cited by in corpus (33)

• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• On topological phases of spin chains
• Spinon confinement and the Haldane gap in SU(n) spin chains
• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• Qudit quantum computation on matrix product states with global symmetry
• Supersymmetric Valence Bond Solid States
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Topological quantum phase transition in an S=2 spin chain
• Continuous quantum phase transition between two topologically distinct valence bond solid states associated with the same spin value
• Entanglement and SU(n) symmetry in one-dimensional valence bond solid states
• Spontaneous Parity Violation in a Quantum Spin Chain
• 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
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• Effective field theory for Sp(N) antiferromagnets and its phase structure
• Spin 3/2 dimer model
• Hidden Order and Dynamics in Supersymmetric Valence Bond Solid States -- Super-Matrix Product State Formalism
• Entanglement spectra of q-deformed higher spin VBS states
• The matrix product representation for the q-VBS state of one-dimensional higher integer spin model
• Magnetic phases of spin-3/2 fermions on a spatially anisotropic square lattice
• Hidden Sp(2s+1)- or SO(2s+1)-symmetry and new exactly solvable models in ultracold atomic systems
• Exact renormalization in quantum spin chains
• Spatial Reflection and Associated String Order in Quantum Spin Chains
• Spin-spin correlation functions of the q-VBS state of an integer spin model
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Interrelations among frustration-free models via Witten's conjugation
• On the existence of an energy gap in one-dimensional Lesanovsky's model
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• A brief note on the G${}_2$ Affleck-Kennedy-Lieb-Tasaki chain