$\mathbb{Z}_2$-gauging and self-dualities of the $XX$ model and its cousins

• URL: http://arxiv.org/abs/2503.01831v2
• Date: Mon, 17 Mar 2025 04:36:07 GMT
• Title: $\mathbb{Z}_2$-gauging and self-dualities of the $XX$ model and its cousins
• Authors: Lei Su,
• Abstract summary: We investigate the one-dimensional $XX$ lattice model and its cousins through the lens of momentum and winding $U(1)$ symmetries.<n>We derive the self-dualities of their cousins, including the $XX$ model and the Levin-Gu model, through appropriate gauging procedures.
• Score: 0.6073572808831218
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. Finally, we unify the mapping structures of local conserved charges across these models, providing a comprehensive framework for understanding their symmetries and dualities.

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