Entanglement spectra of q-deformed higher spin VBS states

Abstract

We calculate the reduced density matrix of a block of integer spin-S's in a q-deformed valence-bond-solid (VBS) state. This matrix is diagonalized exactly for an infinitely long block in an infinitely long chain. We construct an effective Hamiltonian with the same spectrum as the logarithm of the density matrix. We also derive analytic expressions for the von Neumann and Rényi entanglement entropies. For blocks of finite length, we calculate the eigenvalues of the reduced density matrix by perturbation theory and numerical diagonalization. These results enable us to describe the effects of finite-size corrections on the entanglement spectrum and entropy in this generalized VBS model.

14 pages, 8 EPS figures

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• Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states
• Negativity in the Generalized Valence Bond Solid State
• Bulk Entanglement Spectrum in Gapped Spin Ladders
• $Q$-Deformed Rainbows: a Universal Simulator of Free Entanglement Spectra