Related papers: Fracton topological order via coupled layers
We introduce the XY checkerboard toric code. It represents a generalization of the $\mathbb{Z}_2$ toric code with two types of star operators with $x$ and $y$ flavor and two anisotropic star sublattices forming a checkerboard lattice. The…
Fractons are gapped point-like excitations in $d=3$ topological ordered phases whose motion is constrained. They have been discovered in several gapped models but a unifying physical mechanism for generating them is still missing. It has…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
Fracton phases exhibit striking behavior which appears to render them beyond the standard topological quantum field theory (TQFT) paradigm for classifying gapped quantum matter. Here, we explore fracton phases from the perspective of defect…
Gapped non-liquid state (also known as fracton state) is a very special gapped quantum state of matter that is characterized by a microscopic cellular structure. Such microscopic cellular structure has a macroscopic effect at arbitrary long…
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
Fracton phases are recent entrants to the roster of topological phases in three dimensions. They are characterized by subextensively divergent topological degeneracy and excitations that are constrained to move along lower dimensional…
Fracton topological order hosts fractionalized point-like excitations (e.g., fractons) that have restricted mobility. In this article, we explore even more bizarre realization of fracton phases that admit spatially extended excitations with…
Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the…
We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of…
We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor U(1) scalar charge theory. This work is motivated by…
As new kinds of stabilizer code models, fracton models have been promising in realizing quantum memory or quantum hard drives. However, it has been shown that the fracton topological order of 3D fracton models occurs only at zero…
Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other…
We investigate two dimensional compactifications of three dimensional fractonic stabilizer models. We find the two dimensional topological phases produced as a function of compactification radius for the X-cube model and Haah's cubic code.…
Motivated by the prediction of fractonic topological defects in a quantum crystal, we utilize a reformulated elasticity duality to derive a description of a fracton phase in terms of coupled vector U(1) gauge theories. The fracton order and…
We describe topologically ordered and fracton ordered states on novel geometries which do not have an underlying manifold structure. Using tree graphs such as the $k$-coordinated Bethe lattice ${\cal B}(k)$ and a hypertree called the…
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…
We introduce and develop a theory of fusion and statistical processes of gapped excitations in Abelian fracton phases. The key idea is to incorporate lattice translation symmetry via its action on superselection sectors, which results in a…
We introduce a class of gapped three-dimensional models, dubbed "cage-net fracton models," which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility. Starting from layers of two-dimensional…
Product code construction is a powerful tool for constructing quantum stabilizer codes, which serve as a promising paradigm for realizing fault-tolerant quantum computation. Furthermore, the natural mapping between stabilizer codes and the…