Anomalies in the velocity of sound of the two-dimensional compressible Hubbard model

The propagation of sound is a powerful tool to characterize phase transitions. We study the velocity of sound in the two-dimensional compressible Hubbard model at finite temperature with cluster dynamical mean-field theory. We find sharp anomalies in the velocity of sound as a function of the interaction strength and doping. We show that these anomalies are a signature of supercritical phenomena. They are concomitant with specific heat anomalies. We predict the existence of sound anomalies at the doping p* where the pseudogap ends in the normal state of hole-doped cuprates.