Rational indices for quantum ground state sectors

DOI10.1063/5.0021511zbMath1456.81478arXiv2001.06458OpenAlexW3120191963MaRDI QIDQ5148677

Sven Bachmann, Alex Bols, Martin Fraas, Wojciech De Roeck

Publication date: 4 February 2021

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

Full work available at URL: https://arxiv.org/abs/2001.06458

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Many-body theory; quantum Hall effect (81V70) Statistical mechanics of solids (82D20) Transport processes in time-dependent statistical mechanics (82C70) Fermionic systems in quantum theory (81V74)

Related Items (10)

The spectral gap of a fractional quantum Hall system on a thin torus ⋮ Exactness of linear response in the quantum Hall effect ⋮ Rigorous index theory for one-dimensional interacting topological insulators ⋮ A bulk spectral gap in the presence of edge states for a truncated pseudopotential ⋮ Dynamical Abelian anyons with bound states and scattering states ⋮ Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems ⋮ Adiabatic evolution of low-temperature many-body systems ⋮ Anomaly non-renormalization in interacting Weyl semimetals ⋮ Lieb-Schultz-Mattis theorem and the filling constraint ⋮ Quasi-locality bounds for quantum lattice systems. II: perturbations of frustration-free spin models with gapped ground states

Cites Work

• Unnamed Item
• Unnamed Item
• Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics
• Universality of the Hall conductivity in interacting electron systems
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization. III
• A short proof of stability of topological order under local perturbations
• Automorphic equivalence within gapped phases of quantum lattice systems
• Index theory of one dimensional quantum walks and cellular automata
• Anyons in an exactly solved model and beyond
• Lieb-Robinson bounds and the exponential clustering theorem
• Spectral gap and exponential decay of correlations
• A classification of quantum Hall fluids
• The index of a pair of projections
• Persistence of exponential decay and spectral gaps for interacting fermions
• A many-body index for quantum charge transport
• Quantization of Hall conductance for interacting electrons on a torus
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• A multi-dimensional Lieb-Schultz-Mattis theorem
• Symmetry classes of disordered fermions
• The ℤ2 index of disordered topological insulators with time reversal symmetry
• Nobel Lecture: Fractional quantization
• Note on linear response for interacting Hall insulators
• Matrix product unitaries: structure, symmetries, and topological invariants
• Periodic table for topological insulators and superconductors
• The noncommutative geometry of the quantum Hall effect
• Spectral Flows of Dilations of Fredholm Operators
• Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
• Local perturbations perturb—exponentially–locally
• The stability of free fermi Hamiltonians

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