Approximate Symmetry-Driven Fracton Phase Transitions

Armas & Jain (2023) developed theories for approximate higher-form symmetries, but did not apply them to fractons—systems with restricted mobility (Zhu et al. 2022). This research investigates whether "pseudo-spontaneous" breaking of approximate 1-form symmetries drives fracton confinement transitions, challenging Zhu et al.'s focus on exact symmetries. For instance, in a perturbed X-cube model, we'd analyze how weak explicit symmetry breaking (e.g., subleading terms in the Hamiltonian) alters the first-order transitions Zhu observed. This connects to Huxford et al.'s (2023) findings on unconventional confinement in toric codes, suggesting that fracton phases with approximate symmetries might host hybrid criticality (part first-order, part continuous). The novelty lies in using hydrodynamic defect proliferation (from Armas & Jain) to model fracton melting, potentially revealing new scaling laws beyond Landau-Ginzburg-Wilson paradigms.

References:

1. Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model. Joe Huxford, D. X. Nguyen, Yong Baek Kim (2023). SciPost Physics.
2. Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States.. Guo-Yi Zhu, Ji-Yao Chen, P. Ye, S. Trebst (2022). Physical Review Letters.
3. Approximate higher-form symmetries, topological defects, and dynamical phase transitions. J. Armas, Akash Jain (2023). Physical Review D.