Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems
From MaRDI portal
Publication:6189673
DOI10.1007/s11005-023-01767-8arXiv2102.07209OpenAlexW3130172621MaRDI QIDQ6189673
Bruno Nachtergaele, Robert Sims, Amanda Young
Publication date: 8 February 2024
Published in: Letters in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.07209
Applications of selfadjoint operator algebras to physics (46L60) Perturbation theories for operators and differential equations in quantum theory (81Q15) Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Spectral gap and edge excitations of \(d\)-dimensional PVBS models on half-spaces
- Stability of frustration-free Hamiltonians
- Operator methods in mathematical physics. Conference on operator theory, analysis and mathematical physics (OTAMP) 2010, Bedlewo, Poland
- Product vacua and boundary state models in \(d\)-dimensions
- A short proof of stability of topological order under local perturbations
- Automorphic equivalence within gapped phases of quantum lattice systems
- Anyons in an exactly solved model and beyond
- Ground states in relatively bounded quantum perturbations of classical lattice systems
- Persistence of exponential decay and spectral gaps for interacting fermions
- Quantization of conductance in gapped interacting systems
- Perturbation theory for linear operators.
- Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
- General Lieb-Schultz-Mattis type theorems for quantum spin chains
- A \({{\mathbb{Z}}}_2\)-index of symmetry protected topological phases with reflection symmetry for quantum spin chains
- Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states
- Lie-Schwinger block-diagonalization and gapped quantum chains
- Ground subspaces of topological phases of matter as error correcting codes
- 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
- Perturbation theory for parent Hamiltonians of matrix product states
- Propagation of correlations in quantum lattice systems
- Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactions
- Local gap threshold for frustration-free spin systems
- On a Certain Class of Operator Algebras
- Properties of propagation of quantum spin systems
- Divide and conquer method for proving gaps of frustration free Hamiltonians
- An -valued index of symmetry-protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems
- Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk
- A derivation of braided C*-tensor categories from gapped ground states satisfying the approximate Haag duality
- Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
- Rational indices for quantum ground state sectors
- Quasi-locality bounds for quantum lattice systems. I. Lieb-Robinson bounds, quasi-local maps, and spectral flow automorphisms
- Bulk spectrum and K-theory for infinite-area topological quasicrystals
- 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
- Spectral gaps of frustration-free spin systems with boundary
- The classification of symmetry protected topological phases of one-dimensional fermion systems
- Local Noether theorem for quantum lattice systems and topological invariants of gapped states
- Local iterative block-diagonalization of gapped Hamiltonians: A new tool in singular perturbation theory
