Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement

TL;DR

This paper explores the topological and duality properties of CSS codes and fracton models using cluster state measurements, revealing anomaly inflow, symmetry-protected topological order, and novel dualities in quantum and statistical models.

Contribution

It introduces a framework linking CSS codes, foliated cluster states, and dualities, including a generalization of Kramers-Wannier-Wegner duality and non-invertible symmetries.

Findings

Demonstrates anomaly inflow between CSS codes and cluster states

Establishes a generalized duality for CSS-related statistical models

Constructs self-dual subsystem-symmetric quantum models

Abstract

Calderbank-Shor-Steane (CSS) codes are a class of quantum error correction codes that contains the toric code and fracton models. A procedure called foliation defines a cluster state for a given CSS code. We use the CSS chain complex and its tensor product with other chain complexes to describe the topological structure in the foliated cluster state, and argue that it has a symmetry-protected topological order protected by generalized global symmetries supported on cycles in the foliated CSS chain complex. We demonstrate the so-called anomaly inflow between CSS codes and corresponding foliated cluster states by explicitly showing the equality of the gauge transformations of the bulk and boundary partition functions defined as functionals of defect world-volumes. We show that the bulk and boundary defects are related via measurement of the bulk system. Further, we provide a procedure to obtain statistical models associated with general CSS codes via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models with insertion of twist defects. We also study the measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models based on recent proposals in the literature, and demonstrate a non-invertible fusion of duality operators. Using the cluster-state entanglers, we construct the so-called strange correlator for general CSS/fracton models. Finally, we introduce a new family of subsystem-symmetric quantum models each of which is self-dual under the generalized Kramers-Wannier-Wegner duality transformation, which becomes a non-invertible symmetry.