Quantum geometry, localization, and topological bounds of spin fluctuations

TL;DR

This paper explores how dislocations in crystalline materials influence quantum geometry and topological properties of magnons, revealing defect-induced control over localization, topological phases, and the quantum metric.

Contribution

It demonstrates that dislocations can enhance quantum geometry and induce topological phase transitions, linking lattice defects to quantum state topology and magnonic excitations.

Findings

Dislocations significantly enhance the quantum metric.

Defect-induced geometry controls magnon localization and topological protection.

Dislocation-driven geometry enables transitions to disorder-induced topological phases.

Abstract

We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct link between lattice topology and the Hilbert-space geometry of states. We characterize the quantum geometry of topological magnons in ordered arrays of dislocations, demonstrating that defect-induced geometric enhancement controls their localization and topological protection. In disordered arrays, dislocation-driven geometry expands the accessible topological phase space and enables transitions to disorder-induced topological phases. Our results identify the quantum metric as a tunable bridge between crystalline topology, magnonic excitations, and emergent topological matter in aperiodic solid-state and synthetic systems.