Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk - Henheik, Sven Joscha; Teufel, Stefan; Random matrices beyond Wigner-Dyson-Mehta (Forum of Mathematics, Sigma, 2022)
We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.
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Keywords: article; computational mathematics -- discrete mathematics and combinatorics -- geometry and topology -- mathematical physics -- statistics and probability -- algebra and number theory -- theoretical computer science -- analysis