Entanglement spectra of q-deformed higher spin VBS states

TL;DR

This paper computes the entanglement spectra and entropies of q-deformed higher spin VBS states, revealing how finite-size effects influence quantum entanglement in these models.

Contribution

It provides exact and perturbative methods to analyze the entanglement properties of q-deformed VBS states, including finite-size corrections.

Findings

Exact diagonalization of the density matrix for infinite blocks

Analytic expressions for von Neumann and Rényi entropies

Finite-size effects on entanglement spectra and entropy

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 R\'enyi 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.