Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions

DOI10.1007/s00220-020-03878-yzbMath1462.82037arXiv1908.07450OpenAlexW3106815415MaRDI QIDQ2658936

Alessandro Pizzo, Stefano Rossi, Simone Del Vecchio, Jürg Fröhlich

Publication date: 25 March 2021

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

Full work available at URL: https://arxiv.org/abs/1908.07450

zbMATH Keywords

quantum chainsLie-Schwinger conjugations

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Applications of operator theory in the physical sciences (47N50) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20)

Related Items

Local iterative block-diagonalization of gapped Hamiltonians: A new tool in singular perturbation theory ⋮ Lie-Schwinger block-diagonalization and gapped quantum chains ⋮ Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems ⋮ Block-diagonalization of infinite-volume lattice Hamiltonians with unbounded interactions ⋮ Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states

Cites Work

• Unnamed Item
• On many-body localization for quantum spin chains
• Stability of frustration-free Hamiltonians
• An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory
• A short proof of stability of topological order under local perturbations
• Ground states in relatively bounded quantum perturbations of classical lattice systems
• Mott transition in lattice boson models
• Hidden symmetry breaking and the Haldane phase in \(S=1\) quantum spin chains
• Low-temperature phase diagrams of quantum lattice systems. I: Stability for quantum perturbations of classical systems with finitely-many ground states.
• Persistence of exponential decay and spectral gaps for interacting fermions
• Effective interactions due to quantum fluctuations
• On gapped phases with a continuous symmetry and boundary operators
• Lie-Schwinger block-diagonalization and gapped quantum chains
• Lie-Schwinger block-diagonalization and gapped quantum chains: analyticity of the ground-state energy
• Stability of gapped ground state phases of spins and fermions in one dimension
• Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
• Topological quantum order: Stability under local perturbations
• The stability of free fermi Hamiltonians
• Multi-scale Jacobi method for Anderson localization

This page was built for publication: Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions