$\mathbb{Z}_2$ gauging and self-dualities of the $XX$ model and its cousins
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911055337226240 |
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| author | Su, Lei |
| author_facet | Su, Lei |
| contents | In this work, we investigate the one-dimensional $XX$ lattice model and its cousins through the lens of momentum and winding $U(1)$ symmetries. We distinguish two closely related $\mathbb{Z}_2$ symmetries based on their relation to the $U(1)$ symmetries, and establish a web of $\mathbb{Z}_2$-gauging relations among these models, rooted in two fundamental seeds: the $ XY \pm YX$ models. These two seeds, each self-dual under gauging of the respective $\mathbb{Z}_2$-symmetries, possess manifestly symmetric conserved charges, making transparent the connection between the noninvertible symmetries and the Kramers-Wannier duality. By leveraging the self-dualities of these two seed models, we derive the self-dualities of their cousins, including the $XX$ model and the Levin-Gu model, through appropriate gauging procedures. Moreover, under these gauging schemes, the lattice T-duality matrices take the form of the identity matrix. These lattice models flow to the $c =1$ compact boson conformal field theory, with a twist that depends on the lattice size modulo four. Finally, we unify the mapping structures of local conserved charges across these models, providing a comprehensive framework for understanding their symmetries and dualities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01831 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbb{Z}_2$ gauging and self-dualities of the $XX$ model and its cousins Su, Lei Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics In this work, we investigate the one-dimensional $XX$ lattice model and its cousins through the lens of momentum and winding $U(1)$ symmetries. We distinguish two closely related $\mathbb{Z}_2$ symmetries based on their relation to the $U(1)$ symmetries, and establish a web of $\mathbb{Z}_2$-gauging relations among these models, rooted in two fundamental seeds: the $ XY \pm YX$ models. These two seeds, each self-dual under gauging of the respective $\mathbb{Z}_2$-symmetries, possess manifestly symmetric conserved charges, making transparent the connection between the noninvertible symmetries and the Kramers-Wannier duality. By leveraging the self-dualities of these two seed models, we derive the self-dualities of their cousins, including the $XX$ model and the Levin-Gu model, through appropriate gauging procedures. Moreover, under these gauging schemes, the lattice T-duality matrices take the form of the identity matrix. These lattice models flow to the $c =1$ compact boson conformal field theory, with a twist that depends on the lattice size modulo four. Finally, we unify the mapping structures of local conserved charges across these models, providing a comprehensive framework for understanding their symmetries and dualities. |
| title | $\mathbb{Z}_2$ gauging and self-dualities of the $XX$ model and its cousins |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2503.01831 |