A rigorous result showing that an efficiently implementable, KMS-detailed-balance Lindbladian designed to prepare Gibbs states has a spectral gap (for even-parity observables) bounded below by a constant independent of system size, whenever a lattice of weakly interacting fermions has interaction strength below a size-independent threshold, at any temperature. Through a parent-Hamiltonian construction, third quantization, free-fermion stability, and Lieb-Robinson bounds, the constant gap gives a mixing time at most linear in system size, establishing efficient quantum preparation of these fermionic thermal states.
This work proves that a recently proposed, efficiently implementable Lindbladian, a dissipative quantum dynamics satisfying the KMS quantum detailed-balance condition and having a target Gibbs state …