On renormalization and the local gap method for proving frustration-free local spin chains are gapped

DOI10.1063/5.0139298OpenAlexW4390317976MaRDI QIDQ6183543

Unnamed Author, Ari Mizel

Publication date: 4 January 2024

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

Full work available at URL: https://doi.org/10.1063/5.0139298

Mathematics Subject Classification ID

Quantum computation (81P68) 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)

Cites Work

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• Lieb-Robinson bounds and the exponential clustering theorem
• Spectral gap and exponential decay of correlations
• Making almost commuting matrices commute
• Finitely correlated states on quantum spin chains
• The spectral gap for some spin chains with discrete symmetry breaking
• Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets.
• Local gap threshold for frustration-free spin systems
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Almost commuting self-adjoint matrices - a short proof of Huaxin Lin's theorem.
• Gapped and gapless phases of frustration-free spin-12 chains
• Spectral gaps of frustration-free spin systems with boundary

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