Fig. 1: Illustration on obtaining effective quantized description through the interaction annealing procedure.

Realistic Hamiltonian H for bare particle \({c}_{i}^{\dagger }\) typically contains strong fluctuation that masks the dominant physics. Equivalently, the low-energy dynamics can always be described by fully quantized effective \(\tilde{H}\) upon absorbing rapid fluctuations into dressed particles \({\tilde{c}}_{i}^{\dagger }\). The desired effective description can be obtained through the bare description, \({H}^{{\rm{(a)}}}[\{{d}_{i}^{\dagger }\}]\), of a fictitious `interaction annealed' system with suppressed fluctuation, given \({d}_{i}^{\dagger }\)'s resemblance to the dressed particles \({\tilde{d}}_{i}^{\dagger }\) and the “adiabatic connection” between \({\tilde{d}}_{i}^{\dagger }\) and \({\tilde{c}}_{i}^{\dagger }\) (see text).