Topological Goldstone phases of matter

Else, Dominic V.

doi:10.48550/arxiv.2102.08953

Cited by 2 publications

(4 citation statements)

References 15 publications

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“…As previously discussed, for example in Ref. [82], in general "topological terms for Goldstone modes" arise when the symmetry-breaking ground states, viewed as a family of gapped ground states parameterized by the order parameter manifold, are a topologically non-trivial family. Thus, in order to classify quasicrystalline topological phases, which we view as being characterized by the topological term of the phonons and phasons, we want to classify topological families of ground states parameterized by L * .…”

Section: The General Classification Of Quasicrystalline Topological P...mentioning

confidence: 90%

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Quantum many-body topology of quasicrystals

Else¹,

Huang²,

Prem³

et al. 2021

Preprint

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In this paper, we characterize quasicrystalline interacting topological phases of matter i.e., phases protected by some quasicrystalline structure. We show that the elasticity theory of quasicrystals, which accounts for both "phonon" and "phason" modes, admits non-trivial quantized topological terms with far richer structure than their crystalline counterparts. We show that these terms correspond to distinct phases of matter and also uncover intrinsically quasicrystalline phases, which have no crystalline analogues. For quasicrystals with internal U(1) symmetry, we discuss a number of interpretations and physical implications of the topological terms, including constraints on the mobility of dislocations in d = 2 quasicrystals and a quasicrystalline generalization of the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem. We then extend these ideas much further and address the complete classification of quasicrystalline topological phases, including systems with point-group symmetry as well as non-invertible phases. We hence obtain the "Quasicrystalline Equivalence Principle," which generalizes the classification of crystalline topological phases to the quasicrystalline setting.

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Section: The General Classification Of Quasicrystalline Topological P...mentioning

confidence: 90%

“…One might wonder what the topological term of the Goldstone modes has to do with the SPT phase with respect to the residual symmetry. However, in fact one does expect there to be a general relation [82].…”

Section: Crystalline Spts and "Topological Elasticity Theory"mentioning

confidence: 99%

Quantum many-body topology of quasicrystals

Else¹,

Huang²,

Prem³

et al. 2021

Preprint

Self Cite

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“…they support long-wavelength excitations with vanishing frequency. These arise as a consequence of the Nambu-Goldstone (NG) theorem [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

“…Concretely, we study the nodal charge of acoustic phonons in a 2D material at the Γ point [q = (0, 0)] of the Brillouin zone. Allowing the material to flex out-ofplane, the NG theorem [31][32][33][34][35] predicts that three acoustic bands will be degenerate at Γ, forming a triple point. We assume the presence of spinless TRS T throughout (this is discussed in Appendix A 2), e.g.…”

Section: Introductionmentioning

confidence: 99%

Topological continuum charges of acoustic phonons in 2D

Lange,

Bouhon,

Monserrat

et al. 2021

Preprint

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We analyze the band topology of acoustic phonons in 2D materials by considering the interplay of spatial and internal symmetries with additional constraints that arise from the physical context. These supplemental constraints trace back to the Nambu-Goldstone theorem and the requirements of structural stability. We show that this interplay can give rise to previously unaddressed nontrivial nodal charges that are associated with the crossing of the acoustic phonon branches at the center (Γ-point) of the phononic Brillouin zone. We moreover apply our perspective to the concrete context of graphene, where we demonstrate that the phonon spectrum harbors these kinds of nontrivial nodal charges. Apart from its fundamental appeal, this analysis is physically consequential and dictates how the phonon dispersion is affected when graphene is grown on a substrate. Given the generality of our framework, we anticipate that our strategy that thrives on combining physical context with insights from topology should be widely applicable in characterizing systems beyond electronic band theory.

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Topological Goldstone phases of matter

Cited by 2 publications

References 15 publications

Quantum many-body topology of quasicrystals

Quantum many-body topology of quasicrystals

Topological continuum charges of acoustic phonons in 2D

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