ÖPG-CMD Joint Meeting 2026

Integrating non-Abelian structure in usual Euclidean lattices: Cayley Schreier lattices

Sep 23, 2026, 11:45 AM

15m

HS 11.03 (University of Graz)

3) Contributed talk M01 - Electron correlations and phonons in quantum materials Mini-Colloquium

Speaker

Lavi Kumar Upreti (University of Zurich)

Description

Most condensed matter physics happens on lattices with commuting translations—move right then up equals up then right. But hyperbolic lattices break this: translations become non-Abelian (NAB) or non-commutative, bringing remarkable physics—novel phases from single particle to many-body, superior quantum error correction. Problem: hyperbolic lattices need exponentially growing connections, impractical to scale.

We propose Cayley Schreier lattices (CSL): NAB translations in flat space without curvature. The trick is algebraic—replace each lattice site with n internal states corresponding to n group elements of a group. We will consider one such a group quaternion Q8.