Quantum antiferromagnetic Heisenberg half-odd integer spin model as the entanglement Hamiltonian of the integer spin Affleck-Kennedy-Lieb-Tasaki states

TL;DR

This paper explores how the entanglement Hamiltonian of integer spin AKLT states reveals topological properties and criticality, connecting bulk topological phases with edge states and fractionalized excitations.

Contribution

It demonstrates that the entanglement Hamiltonian of AKLT states corresponds to quantum antiferromagnetic Heisenberg models, elucidating the link between topological phases and quantum criticality.

Findings

EH for even spins describes Haldane gapped phase

EH for odd spins corresponds to half-odd integer spin model with spinons

Topological bulk properties determine edge states and criticality

Abstract

Applying a symmetric bulk bipartition to one-dimensional Affleck-Kennedy-Lieb-Tasaki valence bond solid (VBS) states for the integer spin-S Haldane gapped phase, we can create an array of fractionalized spin-S/2 edge states with the super unit cell $l$ in the reduced bulk system, and the topological properties encoded in the VBS wave functions can be revealed. The entanglement Hamiltonian (EH) with $l=even$ corresponds to the quantum antiferromagnetic Heisenberg spin-S/2 model. For the even integer spins, the EH still describes the Haldane gapped phase. For the odd integer spins, however, the EH just corresponds to the quantum antiferromagnetic Heisenberg half-odd integer spin model with spinon excitations, characterizing the critical point separating the topological Haldane phase from the trivial gapped phase. Our results thus demonstrate that the topological bulk property not only determines its fractionalized edge states, but also the quantum criticality associated with the topological phase, where the elementary excitations are precisely those fractionalized edge degrees of freedom confined in the bulk of the topological phase.