Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. (18th January 2022)

• Record Type: Journal Article
• Authors: Henheik, Joscha; Teufel, Stefan
• Is Part Of: Forum of mathematics. Volume 10(2022)
• Publication Date: 2022-01-18
• Subjects: 81V70 -- 81Q15 -- 81Q99; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2021.80
• Languages: English
• ISSNs: 2050-5094

Abstract

Abstract: 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.