On electronic and magnetic properties of distorted kagome lattices

Abstract

Many-body physics, frustrated magnetism and the knobs for tuning quantum materials intersect at a rich frontier of modern condensed matter physics. The kagome lattice, with its unique geometry and yet not completely understood phase diagram, has emerged as a key platform for exploring such phenomena. In this thesis, we investigate the effects of applied distortions on the magnetic properties of kagome lattices, focusing on the interplay between Geometric Frustration (GF) and correlations. We study a simple Hubbard model, and employ the Density Matrix Renormalization Group (DMRG) method to study the ground state properties of strained kagome systems. Two quantifiers for GF are proposed, and their predictive capabilities evidenced. Based on the literature review we conducted, one of said quantifiers features as the first local correlation-only way to "probe" GF. Our findings are thus a proof of concept in favor of not only that strain can significantly change "effective dimensionalities" and magnetic order, but also modify the "frustration content" and electronic structure of interacting kagome lattices, potentially leading to novel phases and emergent phenomena. This work paves the way for future studies on the interplay between strain, electronic correlations, frustration and elastic properties in interacting kagome lattices, with potential implications for the design of novel quantum materials and devices.