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In this letter we present a unified derivation of the pressure equation ofstates, thermodynamics and scaling functions for the one-dimensional (1D)strongly attractive Fermi gases with $SU(w)$ symmetry. These physicalquantities provide a rigorous understanding on a universality class of quantumcriticality characterised by the critical exponents $z=2$ and correlationlength exponent $\nu=1/2$. Such a universality class of quantum criticality canoccur when the Fermi sea of one branch of charge bound states starts to fill orbecome gapped at zero temperature. The quantum critical cone can be determinedthrough the double peaks in specific heat which serve to mark two crossovertemperatures fanning out from the critical point. Our method opens to furtherstudy on quantum phases and phase transitions in strongly interacting fermionswith large $SU(w)$ and non-$SU(w)$ symmetries in one dimension.

A unified approach to the thermodynamics and quantum scaling functions of one-dimensional strongly attractive $SU(w)$ Fermi Gases