article published yes Sven Joscha Henheik author 31d731d7-d235-11ea-ad11-b50331c8d7fb0000-0003-1106-327X Tom Wessel author LaEr department Random matrices beyond Wigner-Dyson-Mehta project We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs. https://research-explorer.ista.ac.at/download/12184/12410/2022_JourMathPhysics_Henheik2.pdf application/pdfno AIP Publishing2022 eng 0022-2488 2208.12220 00090577620000110.1063/5.0123441 6312 https://research-explorer.ista.ac.at/record/19540 S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022). Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12, 121101, AIP Publishing, 2022, doi:<a href="https://doi.org/10.1063/5.0123441">10.1063/5.0123441</a>. S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice systems,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12. AIP Publishing, 2022. Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems. <i>Journal of Mathematical Physics</i>. 2022;63(12). doi:<a href="https://doi.org/10.1063/5.0123441">10.1063/5.0123441</a> Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101. Henheik, S. J., &#38; Wessel, T. (2022). On adiabatic theory for extended fermionic lattice systems. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href="https://doi.org/10.1063/5.0123441">https://doi.org/10.1063/5.0123441</a> Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href="https://doi.org/10.1063/5.0123441">https://doi.org/10.1063/5.0123441</a>. 121842023-01-15T23:00:52Z2026-07-29T13:18:16Z