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We prove an adiabatic theorem for general densities of observables that are sums of local terms in finite systems of interacting fermions, without periodicity assumptions on the Hamiltonian and with error estimates that are uniform in the size of the system.
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M. Hastings and X.-G. Wen: Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance. Physical Review B 72:045141 (2005)
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S. Bachmann, S. Michalakis, B. Nachtergaele, and R. Sims: Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems. Communications in Mathematical Physics 309:835–871 (2012)
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B. Nachtergaele, V. Scholz, and R. Werner: Local approximation of observables and commutator bounds. Operator Methods in Mathematical Physics. Springer Basel, 2013. 143–149
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H. Schulz-Baldes and S. Teufel: Orbital Polarization and Magnetization for Independent Particles in Disordered Media. Communications in Mathematical Physics 319:649–681 (2013)
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A. Giuliani, V. Mastropietro, and M. Porta: Universality of the Hall Conductivity in Interacting Electron Systems. Communications in Mathematical Physics 349:1107–1161 (2017)
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M. Hastings: The Stability of Free Fermi Hamiltonians. Preprint available at arXiv:1706.02270 (2017)
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S. Bachmann, A. Bols, W. De Roeck, and M. Fraas: Quantization of conductance in gapped interacting systems. Annales Henri Poincaré 19:695–708 (2018)
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S. Bachmann, W. De Roeck, and M. Fraas: The adiabatic theorem and linear response theory for extended quantum systems. Communications in Mathematical Physics 361:997–1027 (2018)
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W. de Roeck and M. Salmhofer: Persistence of exponential decay and spectral gaps for interacting fermions. To appear in Communications in Mathematical Physics, DOI 10.1007/s00220-018-3211-z (2018)
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J. Fröhlich: Chiral Anomaly, Topological Field Theory, and Novel States of Matter. Reviews in Mathematical Physics 30:1840007 (2018)
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