2025/10/23 by Becker, Lennart, Teufel, Stefan, Wesle, Marius
#81V70 #81V74 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2510.20914
We prove an adiabatic theorem for infinitely extended lattice fermion systems with gapped ground states, allowing perturbations that may close the gap. The Heisenberg dynamics on the CAR-algebra is generated by a time dependent two-parameter family of Hamiltonians Hε,ηt=η-1(Ht+ε(H1t+Vt)), where Ht is assumed to have a gapped ground state ωt, η∈ (0,1] is the adiabatic parameter and ε ∈ [0,1] controls the strength of the perturbation. We construct a quasi-local dressing transformation βε,ηt=exp(i LSε,ηt) that yields super-adiabatic states ωε,ηt =ωt ∘ βε,ηt which, when tested against local observables, solve the corresponding time-dependent Schrödinger equation up to errors asymptotically smaller than any power of η and ε. The construction is local in space and time, does not assume uniqueness of the ground state, and works under super-polynomial decay of the interactions Ht and Ht1 rather than exponential decay. If the Hamiltonian is time-independent on an interval, the dressed state is η-independent and forms a non-equilibrium almost-stationary state with lifetime of order ε-∞. The result provides a rigorous basis for linear response to macroscopic changes in gapped systems, including a proof of Ohm's law for macroscopic Hall currents.