Constructing Bulk Topological Orders via Layered Gauging

• URL: http://arxiv.org/abs/2604.27363v1
• Date: Thu, 30 Apr 2026 03:19:28 GMT
• Title: Constructing Bulk Topological Orders via Layered Gauging
• Abstract summary: topological holography relates symmetries in $k$ dimensions to "bulk" topological orders in $(k+1)$ dimensions.<n>We propose a physically intuitive and versatile method to generate $(k+1)$-dimensional topological orders from $k$-dimensional generalized symmetries.<n>We have successfully implemented the method in a number of examples in different spatial dimensions, with symmetries that are conventional, higher-form, subsystem, anomalous, nonabelian, or noninvertible.
• Score: 7.146268503923298
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates symmetries in $k$ dimensions to "bulk" topological orders in $(k+1)$ dimensions. While conceptually profound, most existing bulk construction methods rely on sophisticated mathematical formalisms and can be difficult to apply to certain symmetry types. In this work, we propose a physically intuitive and versatile method, termed the layered gauging construction, to systematically generate $(k+1)$-dimensional (liquid or fracton) topological orders from $k$-dimensional generalized symmetries. Roughly speaking, the prescription is to stack many layers of $k$-dimensional quantum systems with certain symmetries into a $(k+1)$-dimensional pile, and then sequentially gauge a diagonal symmetry acting on each nearest-neighbor pair of layers. The detailed procedure depends on the specific symmetry types. We have successfully implemented the method in a number of examples in different spatial dimensions, with symmetries that are conventional, higher-form, subsystem, anomalous, nonabelian, or noninvertible. We hence conjecture the method to be very general. For example, from the subsystem symmetry of the $2d$ plaquette Ising model, we derive the X-cube model and also an anisotropic fracton topological order. Additionally, starting from an anomalous $\mathbb Z_2$ symmetry in $1d$, we construct a new square lattice model realizing the double semion topological order.

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