  While highly evolved cataclysmic variables (CVs) with brown dwarf donors,
often called "period bouncers", are predicted to make up $\simeq40-70$ % of the
Galactic CV population, only a handful of such systems are currently known. The
identification and characterization of additional period bouncers is therefore
important to probe this poorly understood phase of CV evolution. We investigate
the evolution of the CV QZ Lib following its 2004 super-outburst using
multi-epoch spectroscopy. From time-resolved spectroscopic observations we
measure the orbital period of the system, $P_\mathrm{orb}= 0.06436(20)$ d,
which, combined with the superhump period $P_\mathrm{SH}= 0.064602(24)$ d,
yields the system mass ratio, $q = 0.040(9)$. From the analysis of the spectral
energy distribution we determine the structure of the accretion disc and the
white dwarf effective temperature, $T_\mathrm{eff} = 10\,500 \pm
1500\,\mathrm{K}$. We also derive an upper limit on the effective temperature
of the secondary, $T_\mathrm{eff} \lesssim 1700\,\mathrm{K}$, corresponding to
a brown dwarf of T spectral type. The low temperature of the white dwarf, the
small mass ratio and the fact that the donor is not dominating the
near-infrared emission are all clues of a post bounce system. Although it is
possible that QZ Lib could have formed as a white dwarf plus a brown dwarf
binary, binary population synthesis studies clearly suggest this scenario to be
less likely than a period bouncer detection and we conclude that QZ Lib is a CV
that has already evolved through the period minimum.
