Topological terms of (2+1)d flag-manifold sigma models

Kobayashi, Ryohei; Lee, Yasunori; Shiozaki, Ken; Tanizaki, Yuya

doi:10.1007/jhep08(2021)075

Cited by 11 publications

(9 citation statements)

References 49 publications

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“…instantons. The Z 2 invertible hopfion symmetry reduces to the discrete θ-angles and the full non-invertible hopfion symmetry reduces to the couplings of the 3d CP 1 sigma model to topological orders [31,32]. Therefore, our work suggests that solitonic symmetry in a higher-dimensional spacetime and couplings with topological phases in a lower-dimensional spacetime are described by a unified language.…”

mentioning

confidence: 78%

Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT

Chen¹,

Tanizaki²

2022

Preprint

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Solitonic symmetry is believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover this phenomenon in a concrete quantum field theory, the 4d CP 1 model. This model has two kinds of solitonic excitations, vortices and hopfions, which would follow two U (1) solitonic symmetries according to homotopy groups. Nevertheless, we demonstrate the nonexistence of the hopfion U (1) symmetry by evaluating the hopfion charge of vortex operators. We clarify that what conserves hopfion numbers is a non-invertible symmetry generated by 3d spin topological quantum field theories (TQFTs). Its invertible subgroup is just Z2, which we recognize as a spin bordism invariant. Compared with the 3d CP 1 model, our work suggests a unified description of solitonic symmetries and couplings to topological phases.

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mentioning

confidence: 78%

Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT

Chen¹,

Tanizaki²

2022

Preprint

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“…Such sigma models have recently also been evaluated from a Flag manifold perspective, as in this work (see e.g. Ref [93]). It would therefore be interesting to investigate whether these mathematical results find solid ground in the context we have considered.…”

Section: Discussionmentioning

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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“…[29,30]. However, it has been shown that such a Hopf-like term cannot appear in the Lagrangian of the relativistic SU (3)/U (1) 2 sigma model, as long as it satifies the unitarity and locality axioms of QFT [31] (see also Refs. [32][33][34]).…”

Section: Absence Of Topological Termsmentioning

confidence: 99%

“…Ref. [31] has shown that there are two Chern-Simons terms as possible topological terms, but it is also shown that they cannot appear without explicit breaking of the underlying lattice symmetry.…”

Section: Absence Of Topological Termsmentioning

confidence: 99%

“…So far, we have only used the U (1) 2 gauge invariance and the P SU (3) spin rotational symmetry, so we constrain the possible terms by using the lattice symmetry in the following. As a consequence of the one-unit lattice translation, the subscripts α = 1, 2, 3 must enter equally in Lagrangian for Z 3 cyclic symmetry (31) to hold. The allowed distinct terms can be obtained from (B7) and (B8):…”

Section: Appendix B: Uniqueness Of the Effective Lagrangianmentioning

confidence: 99%

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Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice

Takahashi,

Tanizaki

2021

Preprint

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Using field-theoretic techniques, we study the SU (3) analogue of anti-ferromagnetic Heisenberg spin model on the triangular lattice putting the p-box symmetric representation on each site. Taking the large-p limit, we show that the low-energy effective theory is described by a (2 + 1)-dimensional relativistic SU (3)/U (1) 2 nonlinear sigma model. Since the target space has a nontrivial homotopy π2(SU (3)/U (1) 2 )Z 2 , this model has two kinds of magnetic skyrmions, which can be created and annihilated by monopole instantons. By careful analysis of the Wess-Zumino term in the spin coherent path integral, we compute the Berry phase for these monopoles and it produces the destructive interference. This restricts possible perturbations of the effective Lagrangian by monopole operators, and we see that the valence-bond-solid (VBS) phase should have degenerate ground states when p ∈ 3Z. We also compute 't Hooft anomalies to constrain possible phases of this system, and a direct phase transition between Néel and VBS phases is supported from the anomaly matching.

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Topological terms of (2+1)d flag-manifold sigma models

Cited by 11 publications

References 49 publications

Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT

Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT

Topological continuum charges of acoustic phonons in 2D

Sigma-model analysis of $SU(3)$ antiferromagnetic spins on the triangular lattice

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