Order and Disorder in AKLT Antiferromagnets in Three Dimensions

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.

7 pages, 2 figures

References in corpus (4)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Dipolar spin correlations in classical pyrochlore magnets
• SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
• Simplex solid states of SU(N) quantum antiferromagnets

Cited by in corpus (16)

• Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Quantum spin systems for measurement-based quantum computation
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions
• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• Two-dimensional Valence Bond Solid (AKLT) states from $t_{2g}$ electrons
• AKLT models on decorated square lattices are gapped
• AKLT Models with Quantum Spin Glass Ground States
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• A Bionic Coulomb Phase on the Pyrochlore Lattice
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs