Symmetry Enriched Fracton Phases from Supersolid Duality

Leo Radzihovsky; Michael Pretko

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Symmetry Enriched Fracton Phases from Supersolid Duality

Michael Pretko, Leo Radzihovsky

Strongly Correlated Electrons · Submitted 16 Aug 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.40 · mentions code or data availability 0.02.

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Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms. We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order. The gauge dual describes a fracton state of matter with full dipole mobility endowed by the superfluid order, as governed by "mutual" axion electrodynamics between the fracton and vortex sectors of the theory, with an associated generalized Witten effect. Vortex condensation restores U(1) symmetry, confines dipoles to be subdimensional (recovering the dislocation glide constraint of a commensurate quantum crystal), and drives a phase transition between two distinct fracton phases. Meanwhile, condensation of elementary fracton dipoles and charges, respectively, provide a gauge dual description of the super-hexatic and ordinary superfluid. Consistent with conventional wisdom, in the absence of crystalline order, U(1)-symmetric phases are prohibited at zero temperature via a mechanism akin to deconfined quantum criticality.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms.	contribution 0.46	0.80	0.07	asserted 0.96
s1	We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order.	result 0.51	0.95	0.30	asserted 1.00
s2	The gauge dual describes a fracton state of matter with full dipole mobility endowed by the superfluid order, as governed by "mutual" axion electrodynamics between the fracton and vortex sectors of the theory, with an associated generalized Witten effect.	result 0.83	0.83	0.31	asserted 1.00
s3	Vortex condensation restores U(1) symmetry, confines dipoles to be subdimensional (recovering the dislocation glide constraint of a commensurate quantum crystal), and drives a phase transition between two distinct fracton phases.	result 0.88	0.79	0.21	asserted 1.00
s4	Meanwhile, condensation of elementary fracton dipoles and charges, respectively, provide a gauge dual description of the super-hexatic and ordinary superfluid.	result 0.92	0.84	0.12	asserted 0.99
s5	Consistent with conventional wisdom, in the absence of crystalline order, U(1)-symmetric phases are prohibited at zero temperature via a mechanism akin to deconfined quantum criticality.	interpretation 0.52	0.16	0.10	hedged possibility 0.80

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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The paper

Original abstract

Motivated by the recently established duality between elasticity of crystals and a fracton tensor gauge theory, we combine it with boson-vortex duality, to explicitly account for bosonic statistics of the underlying atoms. We thereby derive a hybrid vector-tensor gauge dual of a supersolid, which features both crystalline and superfluid order. The gauge dual describes a fracton state of matter with full dipole mobility endowed by the superfluid order, as governed by "mutual" axion electrodynamics between the fracton and vortex sectors of the theory, with an associated generalized Witten effect. Vortex condensation restores U(1) symmetry, confines dipoles to be subdimensional (recovering the dislocation glide constraint of a commensurate quantum crystal), and drives a phase transition between two distinct fracton phases. Meanwhile, condensation of elementary fracton dipoles and charges, respectively, provide a gauge dual description of the super-hexatic and ordinary superfluid. Consistent with conventional wisdom, in the absence of crystalline order, U(1)-symmetric phases are prohibited at zero temperature via a mechanism akin to deconfined quantum criticality.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Towards classification of Fracton phases: the multipole algebra
cond-mat.str-el 2018-12 conditional novelty 6.0 of 10

A new algebraic framework, the multipole algebra, generates the known symmetric tensor and generalized gauge theories of fracton phases, including a U(1) Haah code, by partial gauging of multipole-moment conservation laws.
Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
cond-mat.str-el 2018-12 conditional novelty 6.0 of 10

A foliated field theory and an exactly solvable string-membrane-net lattice model describe abelian foliated fracton phases, with the lattice model shown equivalent to the X-cube model by an explicit local unitary circuit.
The Fracton Gauge Principle
cond-mat.str-el 2018-07 accept novelty 6.0 of 10

Applying the gauge principle to a field theory of ungauged fractons with conserved charge and dipole moment yields the rank-two symmetric tensor gauge theory of fractons, previously only postulated.
Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
hep-th 2022-05 unverdicted novelty 2.0 of 10

This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
Space-dependent symmetries and fractons
hep-th 2021-12 accept novelty 2.0 of 10

Coordinate-dependent symmetries and elastic dualities provide a unified effective description of gapless fractons, their defects, and their subdiffusive hydrodynamics.

How later papers used it

47 later papers cite it

Evidence: some. 38 of the citing papers share no author with it, and 2 of those carry a confident label from Pith's citation classifier.

Pith read 6 of the 81 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper · 1 by the same authors

By the same authors

Linearized the appearance of the phonon field in this paper by introducing lattice momentum, stress tensor and bond angle fields.

Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries (2023) (same authors) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

18 arXiv papers cite this in 24 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 17 sentences without a confident label

Cites it as background 7 papers

In a somewhat surprising parallel development it was argued that certain type-I fracton models are related to a quantum theory of elasticity [ref] .

Towards classification of Fracton phases: the multipole algebra · Introduction · 0.81
[ref] There are many exciting questions remaining to be answered.

The Fracton Gauge Principle · Introduction · 0.96
Related work: while this manuscript was being prepared several relevant works on symmetry-enforced fractonic matter appeared [ref] .

Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory · Discussion · 0.90

What it cites · 11 sentences without a confident label

Contests 1 paper

Specifically, the tensor-only gauge theory [ref] is incomplete as it does not incorporate the quantum statistics of the constituent particles, which is essential in a fluid state.

Fracton-Elasticity Duality · Introduction · contest 0.71

Builds on 1 paper

This duality combines the newly established fracton-elasticity duality [ref] with conventional particle-vortex duality [ref] into one “mother” duality, featuring both vector and tensor gauge fields, coupled by “mutual” axion terms and exhibiting an associated generalized Witten effect.

Fracton-Elasticity Duality · Introduction · 0.91

Compares with 2 papers

[ref] Similar charge attachment to lattice defects has also been observed in the context of melting transitions in quantum Hall phases.

"Deconfined" quantum critical points · Introduction · 0.80
[ref] Similar charge attachment to lattice defects has also been observed in the context of melting transitions in quantum Hall phases.

Deconfined criticality critically defined · Introduction · 0.80

Cites as background 22 papers

[ref] (We refer the reader to a recent review [ref] and to selected literature [ref] for an overview of fractons.) Phonons map onto the gapless gauge modes, while disclinations and dislocations map onto fracton charges and dipoles, respectively.

Local stabilizer codes in three dimensions without string logical operators · Introduction · 0.90
[ref] (We refer the reader to a recent review [ref] and to selected literature [ref] for an overview of fractons.) Phonons map onto the gapless gauge modes, while disclinations and dislocations map onto fracton charges and dipoles, respectively.

A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations · Introduction · 0.90
[ref] (We refer the reader to a recent review [ref] and to selected literature [ref] for an overview of fractons.) Phonons map onto the gapless gauge modes, while disclinations and dislocations map onto fracton charges and dipoles, respectively.

Fracton Topological Order, Generalized Lattice Gauge Theory and Duality · Introduction · 0.90

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