Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
arXiv:2201.09307 · doi:10.1007/978-3-031-03998-0_5
Abstract
Affleck, Kennedy, Lieb, and Tasaki constructed a spin-1 model that is isotropic in spins and possesses a provable finite gap above the ground state more than three decades ago. They also constructed models in two dimensions. Their construction has impacted subsequent research that is still active. In this review article, we review some selected the progresses, such as magnetic ordering of the AKLT models, emerging phases under deforming the AKLT Hamiltonians, symmetry-protected topological order in several AKLT models, their spectral gap, and applications for quantum computation.
47 pages, single column, 12 figures, to appear in a Chapter of the Springer Volume on Entanglement in Spin Chains - Theory and Quantum Technology Applications
References in corpus (12)
- Multi-party entanglement in graph states
- Entanglement versus Correlations in Spin Systems
- Diverging Entanglement Length in Gapped Quantum Spin Systems
- Observation of fractional edge excitations in nanographene spin chains
- Novel schemes for measurement-based quantum computation
- Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
- Quantum computation on the edge of a symmetry-protected topological order
- Quantum computational capability of a 2D valence bond solid phase
- Optical one-way quantum computing with a simulated valence-bond solid
- Resource quality of a symmetry-protected topologically ordered phase for quantum computation
- Quantum state reduction for universal measurement based computation
- Driven-dissipative control of cold atoms in tilted optical lattices