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

TL;DR

This paper analyzes the entanglement properties of generalized SU(n) valence bond solid states in one dimension, providing a unified and simplified method for calculating various entanglement measures.

Contribution

It introduces a new, elegant approach to evaluate entanglement measures in SU(n) VBS states using transfer matrices and symmetry, extending previous SU(2) results.

Findings

Derived transfer matrix for SU(n) VBS states

Calculated entanglement measures such as entropy and correlation length

Results agree with known SU(2) case

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 R\'enyi 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.