  Quantum phase transitions in quantum matter occur at zero temperature between
distinct ground states by tuning a nonthermal control parameter. Often, they
can be accurately described within the Landau theory of phase transitions,
similarly to conventional thermal phase transitions. However, this picture can
break down under certain circumstances. Here, we present a comprehensive study
of the effect of hydrostatic pressure on the magnetic structure and spin
dynamics of the spin-1/2 ladder compound C$_9$H$_{18}$N$_2$CuBr$_4$.
Single-crystal heat capacity and neutron diffraction measurements reveal that
the N$\rm \acute{e}$el-ordered phase breaks down beyond a critical pressure of
$P_{\rm c}$$\sim$1.0 GPa through a continuous quantum phase transition.
Estimates of the critical exponents suggest that this transition may fall
outside the traditional Landau paradigm. The inelastic neutron scattering
spectra at 1.3 GPa are characterized by two well-separated gapped modes,
including one continuum-like and another resolution-limited excitation in
distinct scattering channels, which further indicates an exotic
quantum-disordered phase above $P_{\rm c}$.
