Quantum Metric Induced Phases in Moir\'e Materials

TL;DR

This paper demonstrates that quantum geometry, especially the Fubini Study metric, crucially influences low-energy phases in strongly correlated moiré materials, leading to symmetry breaking and novel interaction-driven states.

Contribution

It reveals how quantum geometry governs ground states in lattice models at fractional fillings, highlighting the importance of the Fubini Study metric in moiré materials and their emergent phases.

Findings

Quantum geometry determines ground states in lattice models.

Fubini Study metric influences symmetry breaking and Fermi liquids.

Quantum metric effects can simplify strongly coupled problems.

Abstract

We show that, quite generally, quantum geometry plays a major role in determining the low-energy physics in strongly correlated lattice models at fractional band fillings. We identify limits in which the Fubini Study metric dictates the ground states and show that this is highly relevant for Moir\'e materials leading to symmetry breaking and interaction driven Fermi liquids. This phenomenology stems from a remarkable interplay between the quantum geometry and interactions which is absent in continuum Landau levels but generically present in lattice models where these terms tend to destabilize e.g. fractional Chern insulators. We explain this as a consequence of the fundamental asymmetry between electrons and holes for band projected normal ordered interactions, as well as from the perspective of a self-consistent Hartree-Fock calculation. These basic insights about the role of the quantum metric turn, when dominant, an extremely strongly coupled problem into an effectively weakly coupled one, and may also serve as a guiding principle for designing material setups.