Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states
DOI10.1007/s00023-021-01086-5OpenAlexW3195376037MaRDI QIDQ2118815
Bruno Nachtergaele, Robert Sims, Amanda Young
Publication date: 23 March 2022
Published in: Annales Henri Poincaré (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.15337
Statistical mechanics of crystals (82D25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)
Related Items (7)
Cites Work
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- An invariant of topologically ordered states under local unitary transformations
- Spectral gap and edge excitations of \(d\)-dimensional PVBS models on half-spaces
- Stability of frustration-free Hamiltonians
- Product vacua and boundary state models in \(d\)-dimensions
- Quantum spin systems on infinite lattices. A concise introduction
- Uniqueness of the translationally invariant ground state in quantum spin systems
- A short proof of stability of topological order under local perturbations
- Automorphic equivalence within gapped phases of quantum lattice systems
- On the stability of topological phases on a lattice
- A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
- On the spectrum of the Heisenberg Hamiltonian
- Anyons in an exactly solved model and beyond
- Ground states in relatively bounded quantum perturbations of classical lattice systems
- Lieb-Robinson bounds and the exponential clustering theorem
- Spectral gap and exponential decay of correlations
- Mott transition in lattice boson models
- Finitely correlated states on quantum spin chains
- Hidden symmetry breaking and the Haldane phase in \(S=1\) quantum spin chains
- The spectral gap of the ferromagnetic \(XXZ\) chain
- On the spectra of the kink for ferromagnetic \(XXZ\) models
- Improved bounds on the spectral gap above frustration-free Ground states of quantum spin chains
- Low-temperature phase diagrams of quantum lattice systems. I: Stability for quantum perturbations of classical systems with finitely-many ground states.
- The adiabatic theorem and linear response theory for extended quantum systems
- Convergence of sequences of linear operators and their spectra
- Persistence of exponential decay and spectral gaps for interacting fermions
- Quantization of conductance in gapped interacting systems
- Perturbation theory for linear operators.
- The spectral gap for the ferromagnetic spin-\(J\) \(XXZ\) chain
- Fault-tolerant quantum computation by anyons
- The spectral gap for some spin chains with discrete symmetry breaking
- Low temperature phase diagrams for quantum perturbations of classical spin systems
- Energy gaps and elementary excitations for certain VBS-quantum antiferromagnets.
- Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
- A \({{\mathbb{Z}}}_2\)-index of symmetry protected topological phases with reflection symmetry for quantum spin chains
- A many-body index for quantum charge transport
- Lie-Schwinger block-diagonalization and gapped quantum chains
- Lie-Schwinger block-diagonalization and gapped quantum chains: analyticity of the ground-state energy
- Ground subspaces of topological phases of matter as error correcting codes
- Product vacua with boundary states and the classification of gapped phases
- Quantization of Hall conductance for interacting electrons on a torus
- On the stability of charges in infinite quantum spin systems
- Automorphic equivalence within gapped phases in the bulk
- A \(\mathbb{Z}_2\)-index of symmetry protected topological phases with time reversal symmetry for quantum spin chains
- Automorphic equivalence preserves the split property
- Stability of local quantum dissipative systems
- Perturbation theory for parent Hamiltonians of matrix product states
- \(C^1\)-classification of gapped parent Hamiltonians of quantum spin chains
- The complete set of infinite volume ground states for Kitaev's abelian quantum double models
- Existence of phase transitions for quantum lattice systems
- Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems
- Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
- Spectral gaps and incompressibility in a \(\nu = 1/3\) fractional quantum Hall system
- Local gap threshold for frustration-free spin systems
- A class of two-dimensional AKLT models with a gap
- Spectral gap, and split property in quantum spin chains
- Periodic table for topological insulators and superconductors
- Stability of gapped ground state phases of spins and fermions in one dimension
- Physics and Mathematics of Quantum Many-Body Systems
- Rational indices for quantum ground state sectors
- Gapped PVBS models for all species numbers and dimensions
- Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms
- Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
- Topological quantum order: Stability under local perturbations
- Gapped and gapless phases of frustration-free spin-12 chains
- A statistical mechanics view on Kitaev's proposal for quantum memories
- The stability of free fermi Hamiltonians
- Spectral gaps of frustration-free spin systems with boundary
- A new SU(2) anomaly
- A classification of pure states on quantum spin chains satisfying the split property with on-site finite group symmetries
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