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We prove a generalised super-adiabatic theorem for extended fermionic systemsassuming a spectral gap only in the bulk. More precisely, we assume that theinfinite system has a unique ground state and that the correspondingGNS-Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we showthat a similar adiabatic theorem also holds in the bulk of finite systems up toerrors that vanish faster than any inverse power of the system size, althoughthe corresponding finite volume Hamiltonians need not have a spectral gap.

Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk