  Close to a zero temperature transition between ordered and disordered
electronic phases, quantum fluctuations can lead to a strong enhancement of the
electron mass and to the emergence of competing phases such as
superconductivity. A correlation between the existence of such a quantum phase
transition and superconductivity is quite well established in some heavy
fermion and iron-based superconductors and there have been suggestions that
high temperature superconductivity in the copper oxide materials (cuprates) may
also be driven by the same mechanism. Close to optimal doping, where the
superconducting transition temperature $T_c$ is maximum in the cuprates, two
different phases are known to compete with superconductivity: a poorly
understood pseudogap phase and a charge ordered phase. Recent experiments have
shown a strong increase in quasiparticle mass $m^*$ in the cuprate
YBa$_2$Cu$_3$O$_{7-\delta}$ as optimal doping is approached suggesting that
quantum fluctuations of the charge ordered phase may be responsible for the
high-$T_c$ superconductivity. We have tested the robustness of this correlation
between $m^*$ and $T_c$ by performing quantum oscillation studies on the
stoichiometric compound YBa$_2$Cu$_4$O$_8$ under hydrostatic pressure. In
contrast to the results for YBa$_2$Cu$_3$O$_{7-\delta}$, we find that in
YBa$_2$Cu$_4$O$_8$ the mass decreases as $T_c$ increases under pressure. This
inverse correlation between $m^*$ and $T_c$ suggests that quantum fluctuations
of the charge order enhance $m^*$ but do not enhance $T_c$.
