Canossa, GiovanniPollet, LodeMartín-Delgado Alcántara, Miguel ÁngelSong, HaoLiu, Ke2026-04-302026-04-302026-03-27G. Canossa, L. Pollet, M. A. Martin-Delgado, H. Song, and K. Liu, Error resilience of fracton codes and near saturation of code-capacity threshold in three dimensions, Phys. Rev. B 113, 104204 (2026).2469-995010.1103/2y2z-hgfnhttps://hdl.handle.net/20.500.14352/136473Fracton codes have been intensively studied as novel topological states of matter, yet their fault-tolerant properties remain largely unexplored. Here, we investigate the optimal thresholds of self-dual fracton codes, in particular, the checkerboard code, against stochastic Pauli noise. By utilizing a statistical-mechanical mapping combined with large-scale parallel tempering Monte Carlo simulations, we calculate the optimal code-capacity threshold of the checkerboard code to be 𝑝th≃0.107⁢(3). This value is the highest among known three-dimensional codes and nearly saturates the theoretical limit for topological codes. Our results further validate the generalized entropy relation for two mutually dual models, 𝐻⁡(𝑝th)+𝐻⁡(˜𝑝th)≈1, and extend its applicability beyond standard topological codes. This verification indicates the Haah's code also possesses a code-capacity threshold near the theoretical limit 𝑝th≈0.11. These findings highlight fracton codes as highly resilient quantum memory and demonstrate the utility of duality techniques in analyzing intricate error-correcting codes.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal article2469-9969https://doi.org/10.1103/2y2z-hgfnhttps://journals.aps.org/prb/abstract/10.1103/2y2z-hgfnopen access53530.145FractonsPhase transitionsQuantum error correctionDisordered systemsMulticritical pointAccuracy thresholdQuantumDualityModelsFísica (Física)Teoría de los quanta2212 Física Teórica2212.12 Teoría Cuántica de Campos