Higgs like stiffness and fractons on the verge of phase transitions

In condensed matter Physics, massive longitudinal Higgs modes emerge from fluctuations of the order parameter amplitude. A few years ago, the Higgs mode was caught experimentally in the vicinity of an insulator-to-superconductor quantum phase transition [Nat. Phys. 11, 188 (2015)]. Here, we propose, in analogy to the Higgs mode, the concept of Higgs-like stiffness (HLS), which emerges close to both classical and quantum phase transitions as a universal manifestation of matter in this regime. We build up a Landau free energy for the dielectric response function to demonstrate that any complex physical quantity can be used to infer the presence of the HLS. Our analysis is discussed in terms of experimental results of the quasi-static dielectric constant for the $$\text {(TMTTF)}_{2}\text {SbF}_6$$ Fabre salt. Yet, we discuss the emergence of fractons in connection with the locking of particular molecular rotational degrees of freedom and the estimation of distinct critical exponents above and below the Mott-Hubbard ferroelectric transition.