Related papers: Fracton topological order via coupled layers
The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for…
Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…
We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological…
Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms. We thereby derive…
Haah's cubic code is the prototypical type-II fracton topological order. It instantiates the no string-like operator property that underlies the favorable scaling of its code distance and logical energy barrier. Previously, the cubic code…
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 gapped interfaces in X cube model, and the gapped interfaces between the…
In this work, we generalize several three-dimensional Z2 stabilizer models--including the X-cube model, the three-dimensional toric code, and Haah's code--to their ZN counterparts. Under periodic boundary conditions, we analyze their ground…
The X-cube model, a prototypical gapped fracton model, has been shown to have a foliation structure. That is, inside the 3+1D model, there are hidden layers of 2+1D gapped topological states. A screw dislocation in a 3+1D lattice can often…
We introduce exactly solvable models of interacting (Majorana) fermions in $d \ge 3$ spatial dimensions that realize a new kind of topological quantum order, building on a model presented in ref. [1]. These models have extensive topological…
We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions (see cond-mat/0503555; we show how such a system can develop topological order thanks to flux…
Topological phase transitions beyond anyon condensation remain poorly understood. A notable example is the transition between the toric code (TC) and double semion (DS) phases, which has two distinct $\mathbb{Z}_2$ topological orders in (2…
In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases,…
Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and…
Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime…
Following a general protocol of periodically driving static first-order topological phases (supporting surface states) with suitable discrete symmetry breaking Wilson-Dirac masses, here we construct a hierarchy of higher-order Floquet…
We explore a deep connection between fracton order and product codes. In particular, we propose and analyze conditions on classical seed codes which lead to fracton order in the resulting quantum product codes. Depending on the properties…
The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a…
Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between…
We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models. These field…
We propose a procedure that characterizes free-fermion or interacting multipolar higher-order topological phases via their bulk entanglement structure. To this end, we construct nested entanglement Hamiltonians by first applying an…