Fracton Topological Order at Finite Temperature

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.

arXiv comment4.5 pages+ references + supplemental material, 4 figures; v2: added references; minor improvements

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• Subsystem Non-Invertible Symmetry Operators and Defects
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Generating Lattice Non-invertible Symmetries
• Boson-fermion duality with subsystem symmetry
• A symmetry principle for gauge theories with fractons
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• Duality viewpoint of criticality
• Topologically Ordered Steady States in Open Quantum Systems
• Bounded light cone and robust topological order out of equilibrium
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes