Entanglement in an SU(n) Valence-Bond-Solid State

Abstract

We investigate entanglement properties in the ground state of the open/periodic SU($n$) generalized valence-bond-solid state consisting of representations of SU($n$). We obtain exact expression for the reduced density matrix of a block of contiguous spins and explicitly evaluate the von Neumann and the Rényi entropies. We discover that the Rényi entropy is independent of the parameter $\alpha$ in the limit of large block sizes and its value $2\log n$ coincides with that of von Neumann entropy. We also find the direct relation between the reduced density matrix of the subsystem and edge states for the corresponding open boundary system.

16 pages, 2 figures; one reference added

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• Geometric Entanglement in a One-Dimensional Valence Bond Solid State
• Entanglement as geometry and flow
• Valence bond solid states with symplectic symmetry
• Qudit quantum computation on matrix product states with global symmetry
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Generalization of the Haldane conjecture to SU($n$) chains
• Flag manifold sigma models: spin chains and integrable theories
• Entanglement in Valence-Bond-Solid States
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Topological and dynamical properties of a generalized cluster model in one dimension
• Entanglement and SU(n) symmetry in one-dimensional valence bond solid states
• Novel families of $\mathrm{SU}(N)$ AKLT states with arbitrary self-conjugate edge states
• Spontaneous Parity Violation in a Quantum Spin Chain
• Entanglement in valence-bond-solid states on symmetric graphs
• 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
• Quasi-exact quantum computation
• Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Spin 3/2 dimer model
• Topological qubits from valence bond solids
• Hidden Order and Dynamics in Supersymmetric Valence Bond Solid States -- Super-Matrix Product State Formalism
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• SU(3) quantum critical model emerging from a spin-1 topological phase
• 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
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Symmetry protected topological phases in two-orbital SU(4) fermionic atoms
• Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain
• Spin-spin correlation functions of the q-VBS state of an integer spin model
• Entanglement of a alternating bipartition in spin chains: Relation with classical integrable models
• Overlap with the Separable State and Phase Transition in the Dicke Model: Zero and Finite Temperature
• Geometric Entanglement in Valance-Bond-Solid state
• Momentum classification of SU($n$) spin chains using extended Young Tableaux
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Interrelations among frustration-free models via Witten's conjugation
• A brief note on the G${}_2$ Affleck-Kennedy-Lieb-Tasaki chain