The dressed molecules theory for the quasi-two-dimensional quantum anomaly

In this work, the dressed molecules theory is used to describe the two-dimensional quantum anomaly of breathing mode in the recent experimental system\cite{Holten2018,Peppler2018}. With the aid of a beyond mean-field, Gaussian pair fluctuation theory, we employ the dressed molecules states to characterize the axial excited states and the Feshbach molecular states, and propose a complete low energy effective theory. We show that, in the whole crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), our theory can describe the two-dimensional experimental systems precisely in low energe region. We explain the the puzzling experimental observations of the smaller than expected breathing mode frequency perfectly. Our establishment of the dressed molecules theory for 2D fermions is crucial to understand the conformal anomaly in the quasi low-dimensional quantum systems.