Foliated Quantum Field Theory of Fracton Order

Slagle, Kevin

doi:10.48550/arxiv.2008.03852

Cited by 9 publications

(12 citation statements)

References 81 publications

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“…Here we review the continuum field theory description of the X-cube model in [21,8]. 17 The continuum theory of (3+1)d Z N X-cube model consists of two gauge fields 17 Other related presentations of this continuum field theory are discussed in [24][25][26].…”

Section: General Charged Statesmentioning

confidence: 99%

FCC, Checkerboards, Fractons, and QFT

Gorantla,

Lam,

Seiberg

et al. 2020

Preprint

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We consider XY-spin degrees of freedom on an FCC lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding U (1) gauge theory on the FCC lattice. Surprisingly, this U (1) gauge theory is dual to the original spin system. We also analyze a similar Z N gauge theory on that lattice. All these systems are fractonic. The U (1) theories are gapless and the Z N theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics.Our Z 2 FCC gauge theory is the continuum limit of the well known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the Z 2 X-cube model.We find new models and new relations between known models. The Z N FCC gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic Z 2 gauge theory. Also, although for N = 2 this model is dual to two copies of the Z 2 X-cube model, a similar statement is not true for higher N .

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Section: General Charged Statesmentioning

confidence: 99%

FCC, Checkerboards, Fractons, and QFT

Gorantla,

Lam,

Seiberg

et al. 2020

Preprint

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“…In the continuum field theory, they become the Wilson operators of the underlying tensor gauge fields [38,17]. We show that these two subsystem symmetries have a mixed 't Hooft anomaly, which we describe explicitly using the field theory developed in [38,17] (see also [39,23,26]). An immediate consequence of this anomaly is that the two Z N subsystem symmetry operators do not commute with each other, leading to the sub-extensive ground state degeneracy [17].…”

Section: Anomaly Inflow For Subsystem Symmetriesmentioning

confidence: 85%

Anomaly Inflow for Subsystem Symmetries

Burnell,

Devakul,

Gorantla

et al. 2021

Preprint

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We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding bulk is therefore a non-trivial subsystem symmetry protected topological (SSPT) phase. We demonstrate these phenomena in several examples with continuous and discrete subsystem global symmetries, as well as time-reversal symmetry. For each example we describe the boundary anomaly, and present classical continuum actions for the corresponding bulk SSPT phases, which describe the response of background gauge fields associated with the subsystem symmetries. Interestingly, we show that the anomaly does not uniquely specify the bulk SSPT phase. In general, the latter may also depend on how the symmetry and the associated foliation structure on the boundary are extended into the bulk.

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“…[40,41], where it has also been found that curved lattices can result in X-cube fractons gaining mobility [41]. Gapped fracton models (such as the X-cube model) can be defined on a foliated manifold without specifying a metric (for which there is no Riemannian structure) [42][43][44]. In the continuum, a foliation structure can be described in terms of a 1-form foliation field e µ [42].…”

Section: Discussionmentioning

confidence: 99%

“…Gapped fracton models (such as the X-cube model) can be defined on a foliated manifold without specifying a metric (for which there is no Riemannian structure) [42][43][44]. In the continuum, a foliation structure can be described in terms of a 1-form foliation field e µ [42]. It is plausible that edge dislocations are present wherever e µ has nonzero curl (i.e.…”

Section: Discussionmentioning

confidence: 99%

Screw dislocations in the X-cube fracton model

Manoj,

Slagle,

Shirley

et al. 2020

Preprint

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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 + 1D model, there are hidden layers of 2 + 1D gapped topological states. A screw dislocation in a 3 + 1D 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 + 1D 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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Foliated Quantum Field Theory of Fracton Order

Cited by 9 publications

References 81 publications

FCC, Checkerboards, Fractons, and QFT

FCC, Checkerboards, Fractons, and QFT

Anomaly Inflow for Subsystem Symmetries

Screw dislocations in the X-cube fracton model

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