Thouless quantum walks in topological flat bands

TL;DR

This paper explores non-Abelian Thouless pumping to implement topologically rich quantum walks in flat band lattices, revealing novel symmetry-breaking dynamics and connections to Weyl-like equations.

Contribution

It introduces a method to realize quantum walks with topological and geometric features using non-Abelian Thouless pumping on flat band lattices.

Findings

Quantum walks encode topological properties.

Parity symmetry breaking observed in dynamics.

Connection to Weyl-like equations established.

Abstract

Non-Abelian gauge symmetries are cornerstones of modern theoretical physics, underlying fundamental interactions and the geometric structure of quantum mechanics. However, their potential to control quantum coherence, entangle- ment, and transport in engineered quantum systems remains to a large extent unexplored. In this work, we propose utilizing non-Abelian Thouless pumping to realize one-dimensional discrete-time quantum walks on topological lattices char- acterized by degenerate flat bands. Through carefully designed pumping cycles, we implement different classes of holonomic coin and shift operators. This frame- work allows for the construction of quantum walks that encode the topological and geometric properties of the underlying system. Remarkably, the resulting evolution exhibits parity symmetry breaking and gives rise to a dynamical pro- cess governed by a Weyl-like equation, highlighting the deep connection between parity and time-reversal symmetry breaking in the system.