Local gap threshold for frustration-free spin systems

DOI10.1063/1.4962337zbMath1347.81086arXiv1512.00088OpenAlexW2184173364MaRDI QIDQ2825540

Evgeny Mozgunov, David Gosset

Publication date: 13 October 2016

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

Full work available at URL: https://arxiv.org/abs/1512.00088

zbMATH Keywords

Knabe's spectral gap bound

Mathematics Subject Classification ID

Continuum limits in quantum field theory (81T27) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (15)

Quantitatively improved finite-size criteria for spectral gaps ⋮ Entanglement subvolume law for 2D frustration-free spin systems ⋮ Spectral gaps and incompressibility in a \(\nu = 1/3\) fractional quantum Hall system ⋮ Thermalization in Kitaev’s quantum double models via tensor network techniques ⋮ A bulk spectral gap in the presence of edge states for a truncated pseudopotential ⋮ On renormalization and the local gap method for proving frustration-free local spin chains are gapped ⋮ Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems ⋮ Spectral gaps of frustration-free spin systems with boundary ⋮ A class of two-dimensional AKLT models with a gap ⋮ Finite-size criteria for spectral gaps in 𝐷-dimensional quantum spin systems ⋮ Spectral gaps for the two-species product vacua and boundary states models on the \(d\)-dimensional lattice ⋮ The AKLT model on a hexagonal chain is gapped ⋮ Divide and conquer method for proving gaps of frustration free Hamiltonians ⋮ Gapped PVBS models for all species numbers and dimensions ⋮ Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states

Cites Work

• The spectral gap for some spin chains with discrete symmetry breaking
• Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets.
• Exponential decay of correlations implies area law
• Spectral Gap Amplification
• Entanglement versus gap for one-dimensional spin systems
• An area law for one-dimensional quantum systems
• Ground state entanglement in one-dimensional translationally invariant quantum systems
• Gapped and gapless phases of frustration-free spin-12 chains

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