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.
arXiv comment47 pages, single column, 12 figures, to appear in a Chapter of the Springer Volume on Entanglement in Spin Chains - Theory and Quantum Technology Applications
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