RT Journal Article
T1 Exotic symmetry breaking properties of self-dual fracton spin models
A1 Canossa, Giovanni
A1 Pollet, Lode
A1 Martín-Delgado Alcántara, Miguel Ángel
A1 Song, Hao
A1 Liu, Ke
AB Fracton codes host unconventional topological states of matter and are promising for fault-tolerant quantum computation due to their large coding space and strong resilience against decoherence and noise. In this paper, we investigate the ground-state properties and phase transitions of two prototypical self-dual fracton spin models—the tetrahedral Ising model and the fractal Ising model—which correspond to error-correction procedures for the representative fracton codes of type I and type II, the checkerboard code and the Haah's code, respectively, in the error-free limit. They are endowed with exotic symmetry-breaking properties that contrast sharply with the spontaneous breaking of global symmetries and deconfinement transition of gauge theories. To show these unconventional behaviors, which are associated with subdimensional symmetries, we construct and analyze the order parameters, correlators, and symmetry generators for both models. Notably, the tetrahedral Ising model acquires an extended semilocal ordering moment, while the fractal Ising model fits into a polynomial ring representation and leads to a fractal order parameter. Numerical studies combined with analytical tools show that both models experience a strong first-order phase transition with an anomalous 𝐿−(𝐷−1) scaling, despite the fractal symmetry of the latter. Our paper provides a unique understanding of subdimensional symmetry breaking and makes an important step for studying quantum-error-correction properties of the checkerboard and Haah's codes.
PB American Physical Society
YR 2024
FD 2024-03-19
LK https://hdl.handle.net/20.500.14352/137003
UL https://hdl.handle.net/20.500.14352/137003
LA eng
NO G. Canossa, L. Pollet, M. A. Martin-Delgado, H. Song, and K. Liu, Exotic symmetry breaking properties of self-dual fracton spin models, Phys. Rev. Research 6, 013304 (2024).
NO W911NF-14-1-0103;12047503;2019SHZDZX01
NO European Commission
NO German Research Foundation
NO Ministerio de Ciencia, Innovación y Universidades (España)
NO Agencia Estatal de Investigación (España)
NO Ministerio de Economía, Industria y Competitividad (España)
NO Comunidad de Madrid
NO Army Research Office (US)
NO National Natural Science Foundation of China
NO Shanghai Municipal Commission of Science and Technology
DS Docta Complutense
RD 8 jun 2026