Role of On-site and Inter-site Coulomb Interactions in KV$_3$Sb$_5$: A first-principles DFT+$U$+$V$ study

Abstract: Nonlocal Coulomb interactions play a crucial role in stabilizing distinct electronic phases in kagome materials. In this work, we systematically investigate the effects of on-site ($U$) and inter-site ($V$) Coulomb interactions on the electronic structure and stability of charge-density-wave (CDW) phases in the kagome metal KV$_3$Sb$_5$ using density functional theory (DFT+$U$+$V$) calculations. We demonstrate that $V$ promotes the formation and stability of CDW phases, whereas $U$ suppresses these phases, highlighting a fundamental competition between local and nonlocal electronic correlations. By directly comparing our theoretical results with angle-resolved photoemission spectroscopy (ARPES) data, we identify realistic values of $U$ and $V$ that accurately describe the electronic band structure of KV$_3$Sb$_5$. Our findings establish a detailed $U$-$V$ phase diagram for KV$_3$Sb$_5$, offering valuable insights into the correlated electronic states in kagome metals and serving as a foundation for future explorations of correlation-driven phenomena in related materials.