Fractons emerge from many-body systems, featuring subdimensional particles with
restricted mobility. These particles have attracted interest for their roles across disciplines …

A bstract We generalize the idea of symmetry topological field theory (SymTFT) for
subsystem symmetry. We propose the 2-foliated BF theory with level N in (3+ 1) d as …

Decoherence is a major obstacle to the preparation of topological order in noisy
intermediate-scale quantum devices. Here, we show that decoherence can also give rise to …

A bstract This work investigates the gapped interfaces of 3+ 1d fracton phases of matter
using foliated gauge theories and lattice models. We analyze the gapped boundaries and …

Fracton codes host unconventional topological states of matter and are promising for fault-
tolerant quantum computation due to their large coding space and strong resilience against …

As long-range entangled (LRE) quantum matter, topologically ordered phases have
attracted extensive attention in the past few decades [1–6]. Recently, there have been a …

The bulk-boundary correspondence is a hallmark feature of topological phases of matter.
Nonetheless, our understanding of the correspondence remains incomplete for phases with …

In this work, we study unconventional anisotropic topologically ordered phases in 3 d that
manifest type-II fractonic physics along submanifolds. While they behave as usual …

Haah's cubic code is the prototypical type-II fracton topological order. It instantiates the no
stringlike operator property that underlies the favorable scaling of its code distance and …

This paper reports an extensive study of three-dimensional topological ordered phases that
in one of the directions behave like usual topological order concerning mobility of …