SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains

TL;DR

This paper constructs special boundary states in SU(n) conformal field theory using symmetry embeddings, identifies them with ground states of SO(n) AKLT spin chains, and computes their boundary entropy through integrability techniques.

Contribution

It introduces a new class of conformal boundary states beyond the standard approach, linking them to integrable SO(n) AKLT models and calculating their boundary entropy analytically.

Findings

Boundary states possess SO(n) symmetry beyond Cardy states.

Identified boundary states as ground states of SO(n) AKLT spin chains.

Computed boundary entropy using exact overlap formulas.

Abstract

We construct a class of conformal boundary states in the $\mathrm{SU}(n)_1$ Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding $\mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1$. These boundary states are beyond the standard Cardy construction and possess $\mathrm{SO}(n)$ symmetry. The $\mathrm{SU}(n)$ Uimin-Lai-Sutherland (ULS) spin chains, which realize the $\mathrm{SU}(n)_1$ WZW model on the lattice, allow us to identify these boundary states as the ground states of the $\mathrm{SO}(n)$ Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the $\mathrm{SU}(n)$ ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.