The interplay of gauge and matter fields in many-body systems can harbor a plethora of interesting phases that cannot be addressed in analytical methods, and require modern numerical methods. Kitaev model gives a realizable setting for such a study where with applied magnetic field, experiments exhibit a set of novel properties that remained poorly understood. We have studied the Kitaev model within the DMRG method with a magnetic field. We find five distinct phases, among which the most interesting are the amorphous crystal and emergent glass phases. The glassy behavior arises from the slow dynamics of the Z2 fluxes and Majorana fermions, as a consequence of the local constraints. Extending the amorphous crystallized phases to a variety of crystalline orders of flux configurations, we find that the Majorana fermions spectrum is made into nearly flat bands with non-zero topological Chern number and quantum metric. I will discuss the construction of Wannier states for the Majorana fermions for those flat bands. If time permits, I will touch upon my other project on classical fragmentation and spin liquids in classical magnets, where we have developed a framework to understand spin liquids and magnetic moment fragmentation by taking the vector space of spins in the repeating unit-cell of the lattice.