Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation

TL;DR

This paper reviews the progress on AKLT models, focusing on their magnetic properties, phase transitions, topological order, spectral gaps, and applications in quantum computation, highlighting their significance in condensed matter physics.

Contribution

It provides a comprehensive review of recent developments in AKLT models, including new insights into their phases, spectral gaps, and computational applications.

Findings

Magnetic ordering in AKLT models

Emerging phases under Hamiltonian deformation

Spectral gap and quantum computational applications

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.