Geometric stability of topological lattice phases

TL;DR

This paper explores the geometric conditions affecting the stability of fractional quantum Hall-like phases in lattice models, providing numerical evidence that these conditions correlate with phase stability and offering practical guidelines for experiments.

Contribution

It introduces the geometric stability hypothesis, linking geometric conditions to phase robustness, supported by extensive numerical simulations on lattice models.

Findings

Strong correlation between geometric conditions and many-body gap

Identification of key physical factors for phase stability

Guidelines for achieving robust FQH-like phases

Abstract

The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments.