Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems

Abstract

Affleck, Kennedy, Lieb and Taski (AKLT) constructed an exemplary spin-3/2 valence-bond solid (VBS) state on the hexagonal lattice, which is the ground state of an isotropic quantum antiferromagnet and possesses no spontaneous magnetization but finite correlation length. This is distinct from the Néel ordered state of the spin-3/2 Heisenberg model on the same lattice. Niggemann, Klümper and Zittartz then generalized the AKLT Hamiltonian to one family invariant under spin rotation about the z-axis. The ground states of this family can be parameterized by a single parameter that deforms the AKLT state, and this system exhibits a quantum phase transition between the VBS and Néel phases, as the parameter increases from the AKLT point to large anisotropy. We investigate the opposite regime when the parameter decreases from the AKLT point and find that there appears to be a Berezinskii-Kosterlitz-Thouless-like transition from the VBS phase to an XY phase. Such a transition also occurs in the deformation of other types of AKLT states with triplet-bond constructions on the same lattice. However, we do not find such an XY-like phase in the deformed AKLT models on other trivalent lattices, such as square-octagon, cross and star lattices. On the star lattice, the deformed family of AKLT states remain in the same phase as the isotropic AKLT state throughout the whole region of the parameter. However, for two triplet-bond generalizations, the triplet VBS phase is sandwiched between two ferromagnetic phases (for large and small deformation parameters, respectively), which are characterized by spontaneous magnetizations along different axes. Along the way, we also discuss how various deformed AKLT states can be used for the purpose of universal quantum computation.

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• Tensor-entanglement renormalization group approach to 2D quantum systems
• Novel schemes for measurement-based quantum computation
• Universal resources for measurement-based quantum computation
• Algorithms for finite Projected Entangled Pair States
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Quantum computational capability of a 2D valence bond solid phase
• Phase transition of computational power in the resource states for one-way quantum computation
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• Quantum state reduction for universal measurement based computation

Cited by in corpus (12)

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• Symmetry-protected topological phases with uniform computational power in one dimension
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• Universal measurement-based quantum computation in two-dimensional SPT phases
• AKLT models on decorated square lattices are gapped
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• Phase transitions of a 2D deformed-AKLT model
• Finite-size scaling analysis of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• Deformations of the Boundary Theory of the Square Lattice AKLT Model