Quantum robustness of fracton phases

TL;DR

This paper investigates how quantum fluctuations affect fracton phases in the X-Cube model and Haah's code, revealing that phase transitions are strongly first order due to the immobility of fracton excitations.

Contribution

It provides a detailed analysis of quantum phase transitions in fracton models using series expansions and variational methods, highlighting the role of fracton immobility.

Findings

All phase transitions are strongly first order.

Fracton excitations are highly immobile, preventing energy lowering via delocalization.

Quantum fluctuations induce phase transitions between fracton and polarized phases.

Abstract

The quantum robustness of fracton phases is investigated by studying the influence of quantum fluctuations on the X-Cube model and Haah's code, which realize a type-I and type-II fracton phase, respectively. To this end a finite uniform magnetic field is applied to induce quantum fluctuations in the fracton phase resulting in zero-temperature phase transitions between fracton phases and polarized phases. Using high-order series expansions and a variational approach, all phase transitions are classified as strongly first order, which turns out to be a consequence of the (partial) immobility of fracton excitations. Indeed, single fractons as well as few-fracton composites can hardly lower their excitation energy by delocalization due to the intriguing properties of fracton phases, as demonstrated in this work explicitly in terms of fracton quasi-particles.