  Disorder-free localization has recently emerged as a mechanism for ergodicity
breaking in homogeneous lattice gauge theories. In this work we show that this
mechanism can lead to unconventional states of quantum matter as the absence of
thermalization lifts constraints imposed by equilibrium statistical physics. We
study a Kitaev honeycomb model in a skew magnetic field subject to a quantum
quench from a fully polarized initial product state and observe nonergodic
dynamics as a consequence of disorder-free localization. We find that the
system exhibits a subballistic power-law entanglement growth and quantum
correlation spreading, which is otherwise typically associated with
thermalizing systems. In the asymptotic steady state the Kitaev model develops
volume-law entanglement and power-law decaying dimer quantum correlations even
at a finite energy density. Our work sheds light onto the potential for
disorder-free localized lattice gauge theories to realize quantum states in two
dimensions with properties beyond what is possible in an equilibrium context.
