Geometric pumping and dephasing at topological phase transition

Abstract

A measure-preserving formalism (MPF) is constructed and applied to spin/band models, which yield observations about pumping. It occurs at topological phase transition (TPT), i.e., a $Z_2$-flip, suggesting that $Z_2$ can imply bulk effects. The model's asymptotic behavior is analytically solved via MPF. The pumping probability is geometric, fractional, and has a ceiling of $\frac{1}{2}$. Intriguingly, theorems are proved about occurrence conditions, which are linked to the system's dimension and the distinction between rational and irrational numbers. Experimental detection is discussed.

9 pages, 4 figures

References in corpus (6)

• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Wigner flow reveals topological order in quantum phase space dynamics
• Light Quantum Control of Persisting Higgs Modes in Iron-Based Superconductors

Cited by in corpus (4)

• Quantum Liouville's theorem based on Haar measure
• Unveiling Symmetry Instability induced by Topological Phase Transitions
• Quantum geometry embedded in unitarity of evolution: revealing its impacts as geometric oscillation and dephasing in spin resonance and crystal bands
• Position operators in terms of converging finite-dimensional matrices: Exploring their interplay with geometry, transport, and gauge theory