Screw dislocations in the X-cube fracton model

Manoj, Nandagopal; Slagle, Kevin; Shirley, Wilbur; Chen, Xie

doi:10.48550/arxiv.2012.07263

Cited by 4 publications

(6 citation statements)

References 29 publications

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“…Consequently, this theory does not have a smooth L x → ∞ continuum limit, which is a manifestation of the UV/IR mixing of such theories [22,49]. Related phenomena have also been observed in various models, for example, [54][55][56][57]48]. Our example is presumably the simplest setup exhibiting this phenomenon.…”

Section: Introductionmentioning

confidence: 70%

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Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Gorantla,

Lam,

Seiberg

et al. 2022

Preprint

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We study field theories with global dipole symmetries and gauge dipole symmetries. The famous Lifshitz theory is an example of a theory with a global dipole symmetry. We study in detail its 1+1d version with a compact field. When this global symmetry is promoted to a U (1) dipole gauge symmetry, the corresponding gauge field is a tensor gauge field. This theory is known to lead to fractons. In order to resolve various subtleties in the precise meaning of these global or gauge symmetries, we place these 1+1d theories on a lattice and then take the continuum limit. Interestingly, the continuum limit is not unique. Different limits lead to different continuum theories, whose operators, defects, global symmetries, etc. are different. We also consider a lattice gauge theory with a Z N dipole gauge group. Surprisingly, several physical observables, such as the ground state degeneracy and the mobility of defects depend sensitively on the number of sites in the lattice.Our analysis forces us to think carefully about global symmetries that do not act on the standard Hilbert space of the theory, but only on the Hilbert space in the presence of defects. We refer to them as time-like global symmetries and discuss them in detail. These time-like global symmetries allow us to phrase the mobility restrictions of defects (including those of fractons) as a consequence of a global symmetry.

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Section: Introductionmentioning

confidence: 70%

“…Consequently, the L x → ∞ limit is not well defined. This subtlety, which is related to phenomena observed in [54][55][56][57]48], reflects the UV/IR mixing in these theories, as emphasized in [49].…”

Section: Discussionmentioning

confidence: 86%

Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Gorantla,

Lam,

Seiberg

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Relatedly, the continuum φ-theory, or equivalently the continuum A-theory of [7], is robust under perturbations by local operators charged under the momentum/magnetic symmetry. 18 Moreover, operators charged under the winding/electric symmetry are not point-like local operators, so the winding/electric symmetry is also robust. See Table 6 for a comparison with other theories.…”

Section: Fixed Continuum Couplingsmentioning

confidence: 99%

“…In fact, depending on the details of the global symmetry, the ground state degeneracy might not even be monotonic in the system size[4,[13][14][15][16][17][18]11].…”

mentioning

confidence: 99%

The low-energy limit of some exotic lattice theories and UV/IR mixing

Gorantla,

Lam,

Seiberg

et al. 2021

Preprint

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We continue our exploration of exotic, gapless lattice and continuum field theories with subsystem global symmetries. In an earlier paper [1], we presented free lattice models enjoying all the global symmetries (except continuous translations), dualities, and anomalies of the continuum theories. Here, we study in detail the relation between the lattice models and the corresponding continuum theories. We do that by analyzing the spectrum of the theories and several correlation functions. These lead us to uncover interesting subtleties in the way the continuum limit can be taken. In particular, in some cases, the infinite volume limit and the continuum limit do not commute. This signals a surprising UV/IR mixing, i.e., long distance sensitivity to short distance details.

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“…Related problems were studied in [15,16,[22][23][24][25]. Although our approach is different, some of the issues we will address have counterparts in these papers.…”

Section: The Twisted Torusmentioning

confidence: 99%

Fractons with Twisted Boundary Conditions and Their Symmetries

Rudelius,

Seiberg,

Shao

2020

Preprint

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We study several exotic systems, including the X-cube model, on a flat three-torus with a twist in the xy-plane. The ground state degeneracy turns out to be a sensitive function of various geometrical parameters. Starting from a lattice, depending on how we take the continuum limit, we find different values of the ground state degeneracy. Yet, there is a natural continuum limit with a well-defined (though infinite) value of that degeneracy. We also uncover a surprising global symmetry in 2 + 1 and 3 + 1 dimensional systems. It originates from the underlying subsystem symmetry, but the way it is realized depends on the twist. In particular, in a preferred coordinate frame, the modular parameter of the twisted two-torus τ = τ 1 + iτ 2 has rational τ 1 = k/m. Then, in systems based on U (1) × U (1) subsystem symmetries, such as momentum and winding symmetries or electric and magnetic symmetries, the new symmetry is a projectively realized Z m × Z m , which leads to an m-fold ground state degeneracy. In systems based on Z N symmetries, like the X-cube model, each of these two Z m factors is replaced by Z gcd(N,m) .

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Screw dislocations in the X-cube fracton model

Cited by 4 publications

References 29 publications

Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons

The low-energy limit of some exotic lattice theories and UV/IR mixing

Fractons with Twisted Boundary Conditions and Their Symmetries

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