Field theory of higher-order topological crystalline response, generalized global symmetries and elasticity tetrads

Nissinen, Jaakko

doi:10.1016/j.aop.2022.169139

Cited by 8 publications

(2 citation statements)

References 75 publications

(200 reference statements)

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“…The extension of the effective actions in terms of anisotropic 4+1d Chern-Simons like terms with vielbeins and torsion is desirable. In general, the elastic gauge symmetries e a → e a + du a are related to higher-form symmetries that enumerate different lattice directions, planes and (hyper)surfaces [89]. The associated responses require torsional geometric gauge theories with translational and rotational fields in a non-relativistic and crystalline setting, see e.g.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The associated responses require torsional geometric gauge theories with translational and rotational fields in a non-relativistic and crystalline setting, see e.g. [78,64,90,48,63,89,62]. These responses, symmetries, anomalies and their anomaly polynomials in topological matter will be discussed elsewhere, see [84] for discussion for a relativistic model.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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Emergent geometry, torsion and anomalies in non-relativistic topological matter

Nissinen

2023

J. Phys.: Conf. Ser.

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I review and discuss aspects of the interplay of emergent geometry and anomalies in topological semimetals and insulators, focusing on effects of torsion. This correspondence identifies torsional topological responses in terms of anomalies and anomaly related hydrodynamic phenomena involving gauge fields and geometry. I discuss how torsional emergent geometry arises from elastic deformations in crystalline materials and how this background couples to thee low-energy continuum models inherited from lattice models, utilizing the semiclassical expansion. Via the coupling of momentum space topology and emergent vielbein geometry, non-relativistic topological matter can realise new geometrical responses of mixed gauge-gravitational character. The topological low-energy torsional responses depend momentum space geometry, lattice momenta and the regularization and UV completion, provided by the non-relativistic physics and symmetries of topological materials.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Conclusion and Discussionmentioning

confidence: 99%

Emergent geometry, torsion and anomalies in non-relativistic topological matter

Nissinen

2023

J. Phys.: Conf. Ser.

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Classification of interacting Dirac semimetals

Huang,

Yu,

Zhang

2024

Phys. Rev. B

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Topological band theory predicts a Z classification of three-dimensional (3D) Dirac semimetals (DSMs) at the single-particle level. Namely, an arbitrary number of identical bulk Dirac nodes will always remain locally stable and gapless in the single-particle band spectrum, as long as the protecting symmetry is preserved. In this work we find that this single-particle classification for Cn-symmetric DSMs will break down to Zn/gcd(2,n) in the presence of symmetry-preserving electron interactions. Our theory is based on a dimensional reduction strategy which reduces a 3D Dirac fermions to one-dimensional building blocks, i.e., vortex-line modes, while respecting all the key symmetries. Using bosonization technique, we find that there exists a minimal number N=n/gcd(2,n) such that the collection of vortex-line modes in N copies of DSMs can be symmetrically eliminated via four-fermion interactions. While this gapping mechanism does not have any free-fermion counterpart, it yields an intuitive “electron-trion coupling” picture. By developing a topological field theory for DSMs and further checking the anomaly-free condition, we independently arrive at the same classification results. Our theory paves the way for understanding topological crystalline semimetallic phases in the strongly correlated regime. Published by the American Physical Society 2024

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Dimensionless Physics: Planck Constant as an Element of the Minkowski Metric

Volovik

2023

Jetp Lett.

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Diakonov theory of quantum gravity, in which tetrads emerge as the bilinear combinations of the fermionic fields, suggests that in general relativity the metric may have dimension 2, i.e. [gμν] = 1/[L]2. Several other approaches to quantum gravity, including the model of superplastic vacuum and BF-theories of gravity support this suggesuion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action S, interval s, cosmological constant Λ, scalar curvature R, scalar field Φ, etc. Here we are trying to further exploit the Diakonov idea, and consider the dimension of the Planck constant. The application of the Diakonov theory suggests that the Planck constant $$\hbar $$ is the parameter of the Minkowski metric. The Minkowski parameter $$\hbar $$ is invariant only under Lorentz transformations, and is not diffeomorphism invariant. As a result the Planck constant $$\hbar $$ has nonzero dimension – the dimension of length [L]. Whether this Planck constant length is related to the Planck length scale, is an open question. In principle there can be different Minkowski vacua with their own values of the parameter $$\hbar $$. Then in the thermal contact between the two vacua their temperatures obey the analog of the Tolman law: $${{\hbar }_{1}}$$/T1 = $${{\hbar }_{2}}$$/T2.

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Field theory of higher-order topological crystalline response, generalized global symmetries and elasticity tetrads

Cited by 8 publications

References 75 publications

Emergent geometry, torsion and anomalies in non-relativistic topological matter

Emergent geometry, torsion and anomalies in non-relativistic topological matter

Classification of interacting Dirac semimetals

Dimensionless Physics: Planck Constant as an Element of the Minkowski Metric

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