  It is well-known that spontaneous symmetry breaking in one spatial dimension
is thermodynamically forbidden at finite energy density. Here we show that
mirror-symmetric disorder in an interacting quantum system can invert this
paradigm, yielding spontaneous breaking of mirror symmetry only at finite
energy density and giving rise to "mirror-glass" order. The mirror-glass
transition, which is driven by a finite density of interacting excitations, is
enabled by many-body localization, and appears to occur simultaneously with the
localization transition. This counterintuitive manifestation of
localization-protected order can be viewed as a quantum analog of inverse
freezing, a phenomenon that occurs, e.g., in certain models of classical spin
glasses.
