Absence of fractal quantum criticality in the quantum Newman-Moore model

TL;DR

This study investigates the quantum phase transition in the 2D quantum Newman-Moore model, finding evidence for a first-order transition with no gap-closing, contrasting with expectations of fractal quantum criticality.

Contribution

The paper provides the first detailed analysis showing the absence of fractal quantum criticality in this model, identifying a first-order transition instead.

Findings

Level crossing at the self-dual point indicating a first-order transition

No gap-closing observed in high-order series expansions

Ground-state energy analysis supports a first-order phase transition

Abstract

The quantum phase transition between the low-field fracton phase with type-II fracton excitations and the high-field polarized phase is investigated in the two-dimensional self-dual quantum Newman-Moore model. We apply perturbative and numerical linked-cluster expansions to calculate the ground-state energy per site in the thermodynamic limit revealing a level crossing at the self-dual point. In addition, high-order series expansions of the relevant low-energy gaps are determined using perturbative continuous unitary transformations indicating no gap-closing. Our results therefore predict a first-order phase transition between the low-field fracton and the high-field polarized phase at the self-dual point.