Minimal Model of Two-Band Quadratic Band Crossing Capturing Wave Function Geometry

Quantum metric, along with the geometry of the wave functions has received attention in condensed matter physics. In this work, we propose a simple model which captures full geometrical aspect of the general two-band quadratic band crossing points (QBCPs) with minimal parameters. We divide the parameters of the QBCPs into two categories: the parameters that define the energy dispersion or the geometry of the system. We show that the physical quantities of this two-band system, such as the Berry phase, can be expressed using geometric parameters. Furthermore, we design a lattice model that captures various geometry of the wave functions on the Bloch sphere and demonstrates how the geometry change under the additional symmetries.