# Pumping with Symmetry

**Authors:** Julio Andrés Iglesias Martínez, Muamer Kadic, Vincent Laude, Emil Prodan  
**arXiv:** [2306.16401](https://arxiv.org/abs/2306.16401)  
**Date:** 2023-06-28  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.16401v1/

## Key points

- Symmetry enhancement in re-configurable materials and meta-materials
- Deformations leading to higher symmetry class and reduction in dispersion bands
- Spectral resonant gaps closing along singular manifolds with topological charges
- Example of deformation in an acoustic crystal resulting in adiabatic cycle with Chern number and Thouless pumping
- General principle for recognizing and engineering topological adiabatic processes around submanifolds with enhanced symmetries
- Context of frieze groups for studying periodic quasi 1-dimensional physical systems
- Switch from molecular systems to meta-materials with symmetric patterns influencing resonant mode dynamics
- Insights into behavior of re-configurable materials and meta-materials regarding symmetry enhancement and implications for topological adiabatic processes
- Potential applications in complex materials design and engineering.

## Summary

In this study, the authors explore the concept of symmetry enhancement in re-configurable materials and meta-materials. They observe that these materials can undergo deformations that result in an abrupt jump to a higher symmetry class, accompanied by a reduction in the number of dispersion bands of excitations. This phenomenon leads to closings of spectral resonant gaps along singular manifolds in a parameter space which carry topological charges. As an example, they consider a deformation of an acoustic crystal that encircles a $p11g$-symmetric configuration of cavity resonators. This deformation results in an adiabatic cycle that carries a Chern number in the bulk and displays Thouless pumping at the edges. The findings suggest a general principle for recognizing and engineering topological adiabatic processes in complex materials and meta-materials around submanifolds of the parameter space with enhanced symmetries. To further investigate this concept, the authors place their discussion within the context of frieze groups - discrete space-groups appropriate for studying periodic quasi 1-dimensional physical systems - and switch from molecular systems to meta-materials where symmetric patterns generated by resonators' positions, orientations, and shapes influence collective resonant mode dynamics. Overall, this study provides valuable insights into the behavior of re-configurable materials and meta-materials with respect to symmetry enhancement and its implications for topological adiabatic processes. The findings have potential applications in various fields involving complex materials design and engineering.