Topological defect networks for fractons of all types

Aasen, David; Bulmash, Daniel; Prem, Abhinav; Slagle, Kevin; Williamson, Dominic J.

doi:10.1103/physrevresearch.2.043165

Cited by 83 publications

(74 citation statements)

References 108 publications

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“…It would certainly be interesting to consider how this generalizes in higher dimensions. Once this more general scenario is well-understood, we could then apply our results to so-called fracton models, which were recently suggested in [74][75][76] to have an interpretation in terms of defect TQFTs. A related question would be to study invertible domain walls such as duality defects and derive the underlying mathematical structure in category theoretical terms.…”

Section: Jhep07(2021)025mentioning

confidence: 89%

Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases

Bullivant

Delcamp

2021

J. High Energ. Phys.

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We study lattice Hamiltonian realisations of (3+1)d Dijkgraaf-Witten theory with gapped boundaries. In addition to the bulk loop-like excitations, the Hamiltonian yields bulk dyonic string-like excitations that terminate at gapped boundaries. Using a tube algebra approach, we classify such excitations and derive the corresponding representation theory. Via a dimensional reduction argument, we relate this tube algebra to that describing (2+1)d boundary point-like excitations at interfaces between two gapped boundaries. Such point-like excitations are well known to be encoded into a bicategory of module categories over the input fusion category. Exploiting this correspondence, we define a bicategory that encodes the string-like excitations ending at gapped boundaries, showing that it is a sub-bicategory of the centre of the input bicategory of group-graded 2-vector spaces. In the process, we explain how gapped boundaries in (3+1)d can be labelled by so-called pseudo-algebra objects over this input bicategory.

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Section: Jhep07(2021)025mentioning

confidence: 89%

Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases

Bullivant

Delcamp

2021

J. High Energ. Phys.

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“…At least, all the cubic codes [13], the X-cube model, and the checkerboard model [15] have homogeneous topological order; see Section 3.1 below. Rigorous verification is anticipated for other models [6,7] in flat space or general manifolds [4,16].…”

Section: Generalitymentioning

confidence: 92%

“…Beyond this aspect, there is not much that is purely topological in fracton phases: there exist analogs of Wilson loop operators but they only give a many-to-one map into homology groups; continuum field theories have been studied [3][4][5] but complete data of operators on the ground state subspace still depend on geometric details. Recently [6][7][8], it is proposed that fracton phases are obtained by stitching together blocks of conventional topological order (anomalous or not), providing a machinery to write a vast number of examples. This construction requires so many algebraic quantities and parameters, including length scales of constituent blocks, that we are motivated to pause and ask what it means for a many-body state to represent a quantum phase of homogeneous matter.…”

Section: Introductionmentioning

confidence: 99%

A degeneracy bound for homogeneous topological order

Haah

2021

SciPost Phys.

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We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace, rather than on the Hamiltonian, and demands that given a collection of ball-like regions, any linear transformation on the ground space be realized by an operator that avoids the ball-like regions. We derive a bound on the ground state degeneracy \mathcal D𝒟 for systems with homogeneous topological order on an arbitrary closed Riemannian manifold of dimension dd, which reads [ D c (L/a)^{d-2}.] Here, LL is the diameter of the system, aa is the lattice spacing, and cc is a constant that only depends on the isometry class of the manifold, and \muμ is a constant that only depends on the density of degrees of freedom. If d=2d=2, the constant cc is the (demi)genus of the space manifold. This bound is saturated up to constants by known examples.examples.

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“…2 1 It is also possible to understand the minimal structure in terms of the defect network construction of the X-cube model. [31,32] 2 Other boundary conditions of the X-cube model exist where different composite excitations are condensed at the boundary. Ref.…”

Section: Smooth and Rough Boundary Conditionsmentioning

confidence: 99%

Screw dislocations in the X-cube fracton model

et al. 2021

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The X-cube model, a prototypical gapped fracton model, was shown in Ref. [1] to have a foliation structure. That is, inside the 3+1 D model, there are hidden layers of 2+1 D gapped topological states. A screw dislocation in a 3+1 D lattice can often reveal nontrivial features associated with a layered structure. In this paper, we study the X-cube model on lattices with screw dislocations. In particular, we find that a screw dislocation results in a finite change in the logarithm of the ground state degeneracy of the model. Part of the change can be traced back to the effect of screw dislocations in a simple stack of 2+1 D topological states, hence corroborating the foliation structure in the model. The other part of the change comes from the induced motion of fractons or sub-dimensional excitations along the dislocation, a feature absent in the stack of 2+1D layers.

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Topological defect networks for fractons of all types

Cited by 83 publications

References 108 publications

Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases

Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases

A degeneracy bound for homogeneous topological order

Screw dislocations in the X-cube fracton model

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