Non-Abelian nonsymmorphic chiral symmetries

TL;DR

This paper demonstrates how synthetic non-Abelian gauge fields can induce nonsymmorphic chiral symmetries in Hofstadter models, leading to protected degeneracies and topological phases in engineered quantum systems.

Contribution

It introduces a theoretical framework for nonsymmorphic chiral symmetries arising from synthetic gauge fields in an SU(2) Hofstadter model, revealing new topological phenomena.

Findings

Nonsymmorphic chiral symmetries can exhibit non-Abelian algebra.

These symmetries protect Kramer quartet states and four-fold degeneracies.

Boundary conditions influence the topological nature of the insulating phases.

Abstract

The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly-controllable simulations of such systems with tailored gauge fields featuring complex spatial textures. These synthetic gauge fields could introduce synthetic symmetries that do not appear in electronic materials. Here, in an SU(2) non-Abelian Hofstadter model, we theoretically show the emergence of multiple nonsymmorphic chiral symmetries, which combine an internal unitary anti-symmetry with fractional spatial translation. Depending on the values of the gauge fields, the nonsymmorphic chiral symmetries can exhibit non-Abelian algebra and protect Kramer quartet states in the bulk band structure, creating general four-fold degeneracy at all momenta. These nonsymmorphic chiral symmetries protect double Dirac semimetals at zero energy, which become gapped into quantum confined insulating phases upon introducing a boundary. Moreover, the parity of the system size can determine whether the resulting insulating phase is trivial or topological. Our work indicates a pathway for creating topology via synthetic symmetries emergent from synthetic gauge fields.