Renormalization-Inspired Monte Carlo Method & Dislocation-Induced Electronic Flat Bands

<p dir="ltr">In this work, we aim to elucidate the possible phases of complex condensed matter systems driven by competing interactions, high configurational entropy, and non-uniform strain. Specifically, we explore two major themes. In the first project, we develop a framework in which phase-separated atomic clusters serve as renormalization parameters, forming a hierarchical structure of clusters as a function of temperature. This approach accelerates the simulation of species-conserving atomic systems with short-range interactions. By leveraging ideas from the renormalization group, it enhances the efficiency of modeling equilibrium configurations of high-entropy alloys. In the second project, we investigate the effects of dislocation strain fields on electronic dispersion relations, utilizing a field-theoretic description of quantized dislocations and modifying the interaction to model different strain field configurations. Our results demonstrate that dislocation patterning induces anisotropic flat bands in the electronic dispersion under specific strain fields and directions, referred to as "magic'' parameters. These flat bands acquire nonzero curvature as the strain or direction deviates from these magic parameters.</p>