Foliated order parameter in a fracton phase transition

TL;DR

This paper investigates a first-order quantum phase transition in the X-cube fracton model, introducing a foliated order parameter that captures the transition's geometric features and highlights the role of dualities in understanding fracton phases.

Contribution

It introduces a non-local foliated order parameter for fracton phases and demonstrates its effectiveness in characterizing phase transitions, advancing understanding of fracton matter.

Findings

Identified a first-order phase transition in the X-cube model.

Showed global entanglement captures features of fracton phase transitions.

Proposed a geometric foliated order parameter to characterize fracton phases.

Abstract

Finding suitable indicators for characterizing quantum phase transitions plays an important role in understanding different phases of matter. It is especially important for fracton phases where a combination of topology and fractionalization leads to exotic features not seen in other known quantum phases. In this paper, we consider the above problem by studying phase transition in the X-cube model in the presence of a non-linear perturbation. Using an analysis of the ground state fidelity and identifying a discontinuity in the global entanglement, we show there is a first order quantum phase transition from a type I fracton phase with a highly entangled nature to a magnetized phase. Accordingly, we conclude that the global entanglement, as a measure of the total quantum correlations in the ground state, can well capture certain features of fracton phase transitions. Then, we introduce a non-local order parameter in the form of a foliated operator which can characterize the above phase transition. We particularly show that such an order parameter has a geometric nature which captures specific differences of fracton phases with topological phases. Our study is specifically based on a well-known dual mapping to the classical plaquette Ising model where it shows the importance of such dualities in studying different quantum phases of matter.