Order and Disorder in AKLT Antiferromagnets in Three Dimensions

TL;DR

This paper investigates the magnetic order or disorder in AKLT antiferromagnets in three dimensions, revealing that lattice structure and spin magnitude critically influence whether the ground state exhibits order or remains disordered due to quantum fluctuations.

Contribution

It provides a detailed analysis of AKLT states in three dimensions across different lattices, identifying conditions under which they are ordered or disordered, including new disordered models on frustrated lattices.

Findings

All AKLT states on cubic lattices are ordered.

Minimal S=2 AKLT state on diamond lattice is disordered.

Several AKLT states on pyrochlore lattice are disordered.

Abstract

The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O(3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Neel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.