A Comment On Berry Connections

Abstract

When families of quantum systems are equipped with a continuous family of Hamiltonians such that there is a gap in the common spectrum one can define a notion of a Berry connection. In this note we stress that, in general, since the Hilbert bundle defining the family of quantum systems does not come with a canonical trivialization there is in fact not a single Berry connection but rather a family of Berry connections. Two examples illustrate that this remark can have physical consequences.

17 pages. V2: Some silly misprints fixed

References in corpus (10)

• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Helical Metal Inside a Topological Band Insulator
• Twisted equivariant matter
• Orbital magnetoelectric coupling in band insulators
• Electric polarization in a Chern insulator
• Majorana zero modes in dislocations of Sr${}_2$RuO${}_4$
• Unified Topological Response Theory for Gapped and Gapless Free Fermions
• Quantum Theory of Large Systems of Non-Relativistic Matter
• Quantum Mechanics With Noncommutative Amplitudes
• Berry Phase Physics in Free and Interacting Fermionic Systems

Cited by in corpus (11)

• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• BPS Hall Algebra of Scattering Hall States
• Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• Geometry of projected connections, Zak phase, and electric polarization
• Supersymmetric polynomials and algebro-combinatorial duality
• Topological insulators and geometry of vector bundles
• A Study of Berry Connection and Complex Analysis for Topological Characterization
• Gradient expansion of the non-Abelian gauge-covariant Moyal star-product