Fracton Topological Order at Finite Temperature

TL;DR

This paper demonstrates that certain higher-dimensional fracton models, specifically a 4D X-cube model, can maintain topological order at finite temperatures, unlike their 3D counterparts, through a phase transition characterized by symmetry breaking.

Contribution

It introduces the first example of a finite-temperature fracton topological order in higher dimensions and proposes a no-go theorem for such order at finite temperature.

Findings

Finite critical temperature $T_c$ for 4D X-cube model.

Observation of confinement-deconfinement phase transition.

Spontaneous breaking of $Z_2$ one-form subsystem symmetry.

Abstract

As new kinds of stabilizer code models, fracton models have been promising in realizing quantum memory or quantum hard drives. However, it has been shown that the fracton topological order of 3D fracton models occurs only at zero temperature. In this Letter, we show that higher dimensional fracton models can support a fracton topological order below a nonzero critical temperature $T_c$. Focusing on a typical 4D X-cube model, we show that there is a finite critical temperature $T_c$ by analyzing its free energy from duality. We also obtained the expectation value of the 't Hooft loops in the 4D X-cube model, which directly shows a confinement-deconfinement phase transition at finite temperature. This finite-temperature phase transition can be understood as spontaneously breaking the $\mathbb{Z}_2$ one-form subsystem symmetry. Moreover, we propose a new no-go theorem for finite-temperature quantum fracton topological order.