Foliated field theory and string-membrane-net condensation picture of fracton order

Abstract

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 mobility restrictions of the topological excitations. In this work, we introduce a new kind of field theory to describe these phases: a foliated field theory. We also introduce a new lattice model and string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order.Contents arXiv:1812.01613v3 [cond-mat.str-el]

Fracton phases of matter

“…[52] with a class of generalized U (1) gauge theories whose charge excitations exhibit fractal structure akin to type-II fracton models [2]. We note that there have also been many other recent developments regarding fractons and field theories, and we refer the interested reader to the literature for details [33,[53][54][55][56][57][58][59]].…”

“…In Ref. 33, a string-membrane-net picture was proposed and was shown to construct models which are equivalent to most of the known foliated fracton models (discussed in the next section) up to trivial degrees of freedom and local unitary transformations.…”

Fracton fusion and statistics

“…However, it is by now a common observation that discrete lattice geometry seems to play a key role in the physics of fracton phases, and it appears that some geometrical structure may be a necessary ingredient of a tractable theory. An important example is the theory of foliated fracton phases [24][25][26][27][28][29], described in more detail below, where geometrical information is provided by a certain kind of foliation structure. Lattice translation imposes a different kind of geometrical structure complementary to that provided by foliation.…”

“…Perhaps the best developed characterizations of gapped fracton phases are those based on the notion of foliated fracton phases [24][25][26][27][28][29]. Some fracton models can be defined on general three-dimensional spatial manifolds with a certain kind of foliation structure.…”

Compactifying fracton stabilizer models

“…It is now widely recognized that fracton phases are sensitive to more than just topology, with their properties depending on certain geometric structures of the underlying manifold [69][70][71][72][73][74][75][76][77]. In this work we only consider translation-invariant fracton models defined on regular cubic lattices.…”