  The accretion behaviour in low-mass X-ray binaries (LMXBs) at low
luminosities, especially at <E34 erg/s, is not well known. This is an important
regime to study to obtain a complete understanding of the accretion process in
LMXBs, and to determine if systems that host neutron stars with
accretion-heated crusts can be used probe the physics of dense matter (which
requires their quiescent thermal emission to be uncontaminated by residual
accretion). Here we examine ultraviolet (UV) and X-ray data obtained when EXO
0748-676, a crust-cooling source, was in quiescence. Our Hubble Space Telescope
spectroscopy observations do not detect the far-UV continuum emission, but do
reveal one strong emission line, Civ. The line is relatively broad (>3500
km/s), which could indicate that it results from an outflow such as a pulsar
wind. By studying several epochs of X-ray and near-UV data obtained with
XMM-Newton, we find no clear indication that the emission in the two wavebands
is connected. Moreover, the luminosity ratio of Lx/Luv >100 is much higher than
that observed from neutron star LMXBs that exhibit low-level accretion in
quiescence. Taken together, this suggests that the UV and X-ray emission of EXO
0748-676 may have different origins, and that thermal emission from
crust-cooling of the neutron star, rather than ongoing low-level accretion, may
be dominating the observed quiescent X-ray flux evolution of this LMXB.
