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Universal Wilson Loop Bound of Quantum Geometry.

Jiabin Yu1,2, Jonah Herzog-Arbeitman2, B Andrei Bernevig2,3,4

  • 1University of Florida, Department of Physics, Gainesville, Florida, USA.

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|September 10, 2025
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Summary
This summary is machine-generated.

We introduce the absolute Wilson loop winding, establishing a lower bound for the quantum metric. This method also bounds superfluid weight, optical conductivity, and band insulator gaps, offering new insights into topological invariants.

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Area of Science:

  • Condensed matter physics
  • Topological materials
  • Quantum field theory

Background:

  • The quantum metric is a key property of topological materials.
  • Existing bounds on the quantum metric, such as Chern and Euler bounds, are known.
  • The role of time-reversal symmetry in bounding topological invariants was an open question.

Purpose of the Study:

  • To define and utilize the absolute Wilson loop winding as a tool.
  • To establish a novel lower bound for the integrated quantum metric.
  • To explore the physical consequences of this bound for various material properties.

Main Methods:

  • Definition of the absolute Wilson loop winding.
  • Mathematical proof of the lower bound for the integrated quantum metric.
  • Application of the bound to time-reversal protected Z2 index and particle-hole Z2 index.

Main Results:

  • The absolute Wilson loop winding provides a lower bound for the integrated quantum metric.
  • This bound reproduces known Chern and Euler bounds.
  • An explicit lower bound for the integrated quantum metric is derived using the time-reversal protected Z2 index.
  • The Z2 bound is shown to bound superfluid weight and optical conductivity from below, and the direct gap of band insulators from above.

Conclusions:

  • The absolute Wilson loop winding offers a versatile method for bounding topological invariants.
  • This work answers an open question regarding the Z2 index and quantum metric.
  • The findings have implications for understanding and designing topological materials with specific electronic and optical properties.