Fracton physics of spatially extended excitations

TL;DR

This paper investigates novel fracton phases with spatially extended excitations that have restricted mobility and deformability, using exactly solvable models to analyze their properties and implications.

Contribution

It introduces exactly solvable lattice models for fracton phases with extended excitations and classifies these excitations into four distinct sectors.

Findings

Identification of four excitation sectors: simple, complex, disconnected, trivial.

Analytical solutions for ground and excited states of the models.

Insights into the properties and implications of extended fracton excitations.

Abstract

Fracton topological order hosts fractionalized point-like excitations (e.g., fractons) that have restricted mobility. In this article, we explore even more bizarre realization of fracton phases that admit spatially extended excitations with restriction on both mobility and deformability. First, we present exactly solvable lattice quantum frustrated spin models and study their ground states and excited states analytically. We construct a family tree in which parent models and descendent models share excitation DNA. Second, with the help of solvability and novel excitation spectrum of these models, we initiate the first-step of general discussions on quantitative and qualitative properties of spatially extended excitations whose mobility and deformability are restricted to some extent. Especially, as a useful viewpoint for understanding such fracton-physics, all excitations are divided into four mutually distinct sectors, namely, simple excitations, complex excitations, intrinsically disconnected excitations, and trivial excitations. Several implications in, e.g., condensed matter physics and gravity are briefly discussed.