Y-cube model and fractal structure of subdimensional particles on hyperbolic lattices

TL;DR

This paper introduces the Y-cube model on hyperbolic lattices, revealing a new type of subdimensional particle called treeons that move on fractal subsets, highlighting the influence of hyperbolic geometry on fracton phases.

Contribution

It generalizes the X-cube model to hyperbolic geometries, discovering treeons and fractal-shaped operators unique to hyperbolic lattices.

Findings

Discovery of treeons on hyperbolic lattices

Fractal-shaped operators can create fractons in hyperbolic space

Treeons reduce to lineons or planeons in flat space

Abstract

Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, dubbed the Y-cube model, on lattices embedded in $H_2\times S^1$ space, i.e., a stack of hyperbolic planes. The name `Y-cube' comes from the Y-shape of the analog of the X-cube's X-shaped vertex operator. We demonstrate that for certain hyperbolic lattice tesselations, the Y-cube model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces treeons becomes either a lineon or a planeon. Intriguingly, we find that for certain hyperbolic tesselations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane.