Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929293119979520 |
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| author | Canossa, Giovanni Pollet, Lode Martin-Delgado, Miguel A. Song, Hao Liu, Ke |
| author_facet | Canossa, Giovanni Pollet, Lode Martin-Delgado, Miguel A. Song, Hao Liu, Ke |
| contents | 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 work, 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 sub-dimensional symmetries, we construct and analyze the order parameters, correlators, and symmetry generators for both models. Notably, the tetrahedral Ising model acquires an extended semi-local 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 work provides new understanding of sub-dimensional symmetry breaking and makes an important step for studying quantum-error-correction properties of the checkerboard and Haah's codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11066 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models Canossa, Giovanni Pollet, Lode Martin-Delgado, Miguel A. Song, Hao Liu, Ke Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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 work, 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 sub-dimensional symmetries, we construct and analyze the order parameters, correlators, and symmetry generators for both models. Notably, the tetrahedral Ising model acquires an extended semi-local 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 work provides new understanding of sub-dimensional symmetry breaking and makes an important step for studying quantum-error-correction properties of the checkerboard and Haah's codes. |
| title | Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2311.11066 |