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Quantum geometric bound and ideal condition for Euler band topology

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Title
Quantum geometric bound and ideal condition for Euler band topology
Author(s)
Kwon, Soonhyun; Bohm-Jung Yang
Publication Date
2024-04
Journal
Physical Review B, v.109, no.16
Publisher
AMER PHYSICAL SOC
Abstract
Understanding the relationship between quantum geometry and topological invariants is a central problem in the study of topological states. In this work, we establish the relationship between the quantum metric and the Euler curvature in two-dimensional systems with space-time inversion IST symmetry satisfying IST2=+1. As IST symmetry imposes the reality of the wave function with vanishing Berry curvature, the well-known inequality between the quantum metric and the Berry curvature is not meaningful in this class of systems. We find that the non-Abelian quantum geometric tensor of two real bands exhibits an intriguing inequality between the off-diagonal Berry curvature and the quantum metric, which in turn gives the inequality between the quantum volume and the Euler invariant. Moreover, we show that the saturation condition of the inequality is deeply related to the ideal condition for Euler bands, which provides a criterion for the stability of fractional topological phases in interacting Euler bands. Our findings demonstrate the potential of the quantum geometry as a powerful tool for characterizing symmetry-protected topological states and their interaction effect. © 2024 American Physical Society.
URI
https://pr.ibs.re.kr/handle/8788114/15192
DOI
10.1103/PhysRevB.109.L161111
ISSN
2469-9950
Appears in Collections:
Center for Correlated Electron Systems(강상관계 물질 연구단) > 1. Journal Papers (저널논문)
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