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

TL;DR

This paper analyzes the entanglement properties of the ground state in SU(n) valence-bond-solid models, providing exact entropy calculations and revealing a universal entropy value related to the system's symmetry.

Contribution

It derives exact reduced density matrices and entropies for SU(n) VBS states, establishing a connection between entanglement and edge states, and showing entropy independence from the Re9nyi parameter.

Findings

Re9nyi entropy is constant for large blocks, equal to 2 log n.

Exact expressions for reduced density matrices are obtained.

A direct relation between subsystem density matrices and edge states is established.

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 R\'enyi entropies. We discover that the R\'enyi 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.