Entanglement and SU(n) symmetry in one-dimensional valence bond solid states

Abstract

Here we evaluate the many-body entanglement properties of a generalized SU(n) valence bond solid state on a chain. Our results follow from a derivation of the transfer matrix of the system which, in combination with symmetry properties, allows for a new, elegant and straightforward evaluation of different entanglement measures. In particular, the geometric entanglement per block, correlation length, von Neumann and Rényi entropies of a block, localizable entanglement and entanglement length are obtained in a very simple way. All our results are in agreement with previous derivations for the SU(2) case.

4 pages, 2 figures

References in corpus (11)

• Entanglement versus Correlations in Spin Systems
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Localizable Entanglement
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Universal geometric entanglement close to quantum phase transitions
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Simplex solid states of SU(N) quantum antiferromagnets
• Entanglement in an SU(n) Valence-Bond-Solid State
• Geometric Entanglement in a One-Dimensional Valence Bond Solid State
• Valence bond solid states with symplectic symmetry

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• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• Topological qubits from valence bond solids
• Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition
• Entanglement spectra of q-deformed higher spin VBS states
• Matrix Product States with long-range Localizable Entanglement
• Entanglement of a alternating bipartition in spin chains: Relation with classical integrable models
• Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry
• Interrelations among frustration-free models via Witten's conjugation