SciPost Submission Page
Intertwined order of generalized global symmetries
by Benjamin Moy, Eduardo Fradkin
Submission summary
| Authors (as registered SciPost users): | Benjamin Moy |
| Submission information | |
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| Preprint Link: | scipost_202503_00065v1 (pdf) |
| Date submitted: | 2025-03-31 20:12 |
| Submitted by: | Moy, Benjamin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We investigate the interplay of generalized global symmetries in 2+1 dimensions in a lattice model that couples a $\mathbb{Z}_N$ clock model to a $\mathbb{Z}_N$ gauge theory via a topological interaction. This coupling binds the charges of one symmetry to the disorder operators of the other, and when these composite objects condense, they give rise to emergent generalized symmetries with mixed 't Hooft anomalies. These anomalies result in phases with ordinary symmetry breaking, topological order, and symmetry-protected topological (SPT) order, where the different types of order are not independent but intimately related. We further explore the gapped boundary states of these exotic phases and develop theories for phase transitions between them. Additionally, we extend this lattice model to incorporate a non-invertible global symmetry, which can be spontaneously broken, leading to domain walls with non-trivial fusion rules.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
Added Refs. 26, 27, 38, 47, 52, 53, 58, 83, and 84
p. 4: Added a citation to Shapere and Wilczek (Ref. 38) and a statement about what they have done
p. 6: Added Footnote 3 and citations to Refs. 8, 47 just after footnote reference. (Also cite Refs. 8, 47 after similar statements on p. 36 and p. 43.)
p. 7: Added citations to Refs. 52, 53
p. 8: Cite Ref. 38 again when introducing the lattice model and add citation to Ref. 58
p. 11: Corrected typo, changing $\xi \to \chi$ in Eq. (2.15). Also cited Ref. 38 for duality.
p. 12: Replaced reference to Appendix C with Appendix B
p. 17: Replaced "integer multiples of $\Theta/2\pi$" with "integer values of $\Theta/2\pi$"
Eq. (2.36): Replaced $a_\mu$ with $k_\mu$ to correct typo
p. 20: Revised discussion of operators that detect symmetry breaking of $\mathbb{Z}_{N}^{(0)}\times \mathbb{Z}_{N}^{(1)} \to $\mathbb{Z}_{N/L}^{(0)}\times \mathbb{Z}_{N/L}^{(1)}$
p. 22: Added Footnote 6.
p. 23: Replaced references to Eq. (4.3) with references to Eq. (4.2). Added "mod $N/L$" to sentence below Eq. (4.4). Added Footnote 7.
p. 24: Replaced $\Phi \to \tilde{\varphi}$, which is now referred to as a dynamical scalar field
Sec. 6.2, Sec. 8, and Appendix A: Replaced $\Phi \to \tilde{\varphi}$ and $C_\mu \to \tilde{c}_\mu$, which are now called dynamical
p. 49: Added Footnote 49 with citations to Refs. 83, 84.
p. 58: Corrected misprint. Replaced "At small $\tilde{g}^2 but large $g^2$ and $e^2$" with "At large $g^2$, $e^2$, and $J$".