The AKLT model on a hexagonal chain is gapped

DOI10.1007/s10955-019-02410-4zbMath1435.82006arXiv1904.01043OpenAlexW3103933004MaRDI QIDQ2283162

Marius Lemm, Anders W. Sandvik, Sibin Yang

Publication date: 30 December 2019

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.01043

zbMATH Keywords

spectral gapquantum computationAKLT (Affleck, Kennedy, Lieb, Tasaki) modelAKLT conjecturecomputer-assisted evaluationfinite-size criterion for spectral gap existenceground states in antiferromagnetsHaldane conjecturehexagonal quantum spin chainspectral gaps for finite subsystems

Mathematics Subject Classification ID

Quantum computation (81P68) Eigenvalues, singular values, and eigenvectors (15A18) Many-body theory; quantum Hall effect (81V70) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical mechanics of magnetic materials (82D40)

Related Items (1)

Quantitatively improved finite-size criteria for spectral gaps

Cites Work

• Quantum computational capability of a 2D valence bond solid phase
• Finitely correlated states on quantum spin chains
• Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets.
• Local gap threshold for frustration-free spin systems
• A class of two-dimensional AKLT models with a gap
• Finite-size criteria for spectral gaps in 𝐷-dimensional quantum spin systems
• Gapped PVBS models for all species numbers and dimensions
• Spectral gaps of frustration-free spin systems with boundary

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