Quantum Inverse Freezing and Mirror-Glass Order

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.