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Register a new userOdd Fracton Theories, Proximate Orders, and Parton Constructions
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The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter must satisfy non-trivial conditions on their low-energy properties when a combination of lattice translation and $U(1)$ symmetry are imposed. We describe a framework to characterize the action of symmetry on fractons and other sub-dimensional fractional excitations, and use this together with the LSM theorem to establish that X-cube fracton order can occur only at integer or half-odd-integer filling. Using explicit parton constructions, we demonstrate that odd
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A powerful mechanism for constructing gauge theories is to start from a theory with a global symmetry, then apply the gauge principle, which demands that this symmetry hold locally. For example, the global phase rotation of a system of conserved charges can be promoted to a local phase rotation by coupling to an ordinary U(1) vector gauge field. More recently, a class of particles has been studied featuring not only charge conservation, but also conservation of higher moments, such as dipole moment, which leads to severe restrictions on the mobility of charges. These particles, called fractons, are known to be intimately connected to symmetric tensor gauge fields. In this work, we show how to derive such tensor gauge theories by applying the gauge principle to a theory of ungauged fractons. We begin by formulating a field theory for ungauged fractons exhibiting global conservation of charge and dipole moment. We show that such fracton field theories have a characteristic non-Gaussian form, reflecting the fact that fractons intrinsically interact with each other even in the absence of a mediating gauge field. We then promote the global higher moment conservation laws to local ones, which requires the introduction of a symmetric tensor gauge field. Finally, we extend these arguments to other types of subdimensional particles besides fractons. This work offers a possible route to the formulation of non-abelian fracton theories.
We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a choice of an Abelian normal subgroup $N$, and a choice of foliation structure. These hybrid fracton orders -- examples of which were introduced in arXiv:2102.09555 -- can also host immobile, point-like excitations that are non-Abelian, and therefore give rise to a protected degeneracy. We construct solvable lattice models for these orders which interpolate between a conventional, three-dimensional $G$ gauge theory and a pure fracton order, by varying the choice of normal subgroup $N$. We demonstrate that certain universal data of the topological excitations and their mobilities are directly related to the choice of $G$ and $N$, and also present complementary perspectives on these orders: certain orders may be obtained by gauging a global symmetry which enriches a particular fracton order, by either fractionalizing on or permuting the excitations with restricted mobility, while certain hybrid orders can be obtained by condensing excitations in a stack of initially decoupled, two-dimensional topological orders.
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.
Fracton topological order (FTO) is a new classification of correlated phases in three spatial dimensions with topological ground state degeneracy (GSD) scaling up with system size, and fractional excitations which are immobile or have restricted mobility. With the topological origin of GSD, FTO is immune to local perturbations, whereas a strong enough global external perturbation is expected to break the order. The critical point of the topological transition is however very challenging to identify. In this work, we propose to characterize quantum phase transition of the type-I FTOs induced by external terms and develop a theory to study analytically the critical point of the transition. In particular, for the external perturbation term creating lineon-type excitations, we predict a generic formula for the critical point of the quantum phase transition, characterized by the breaking-down of GSD. This theory applies to a board class of FTOs, including X-cube model, and for more generic FTO models under perturbations creating two-dimensional (2D) or 3D excitations, we predict the upper and lower limits of the critical point. Our work makes a step in characterizing analytically the quantum phase transition of generic fracton orders.
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 $(k,n)$-hyper-Bethe lattice ${cal HB}(k,n)$ consisting of $k$-coordinated hyperlinks (defined by $n$ sites), we construct multidimensional arboreal arenas such as ${cal B}(k_1) square {cal B}(k_2)$ by the notion of a graph Cartesian product $square$. We study various quantum systems such as the ${mathbb Z}_2$ gauge theory, generalized quantum Ising models (GQIM), the fractonic X-cube model, and related X-cube gauge theory defined on these arenas. Even the simplest ${mathbb Z}_2$ gauge theory on a 2d arboreal arena is fractonic -- the monopole excitation is immobile. The X-cube model on a 3d arboreal arena is fully fractonic, all multipoles are rendered immobile. We obtain variational ground state phase diagrams of these gauge theories. Further, we find an intriguing class of dualities in arboreal arenas as illustrated by the ${mathbb Z}_2$ gauge theory defined on ${cal B}(k_1) square {cal B}(k_2)$ being dual to a GQIM defined on ${cal HB}(2,k_1) square {cal HB}(2,k_2)$. Finally, we discuss different classes of topological and fracton orders on arboreal arenas. We find three distinct classes of arboreal toric code orders on 2d arboreal arenas, those that occur on ${cal B}(2) square {cal B}(2)$, ${cal B}(k) square {cal B}(2), k >2$, and ${cal B}(k_1) square {cal B}(k_2)$, $k_1,k_2>2$. Likewise, four classes of X-cube fracton orders are found in 3d arboreal arenas -- those on ${cal B}(2)square{cal B}(2)square {cal B}(2)$, ${cal B}(k) square {cal B}(2)square {cal B}(2), k>2$, ${cal B}(k_1) square {cal B}(k_2) square {cal B}(2), k_1,k_2 >2$, and ${cal B}(k_1) square {cal B}(k_2) square {cal B}(k_3), k_1,k_2,k_3 >2$.
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