Wilsonian effective field theory of two-dimensional Van Hove singularities

Kapustin, Anton; McKinney, Tristan; Rothstein, Ira Z.

doi:10.1103/physrevb.98.035122

Cited by 7 publications

(5 citation statements)

References 25 publications

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“…This is also a scaleinvariant system; however, its logarithmically-divergent DOS D(E) ∝ ln(Λ/E) raises technical issues in an RG analysis. The non-analyticity of the DOS hinders the RG analysis and the UV cutoff Λ cannot be eliminated from RG equations [18,19]. It occurs as a sequel that the low-energy physics is affected by the UV scale Λ.…”

Section: Summary and Discussionmentioning

confidence: 99%

Supermetal

Isobe

2019

Phys. Rev. Research

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We study the effect of electron interaction in an electronic system with a high-order Van Hove singularity, where the density of states shows a power-law divergence. Owing to scale invariance, we perform a renormalization group (RG) analysis to find a nontrivial metallic behavior where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our RG analysis reveals the Gaussian fixed point and a nontrivial interacting fixed point, which draws an analogy to the φ 4 theory. We further present a finite anomalous dimension at the interacting fixed point by a controlled RG analysis, thus establishing an interacting supermetal as a non-Fermi liquid. arXiv:1905.05188v1 [cond-mat.str-el]

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Section: Summary and Discussionmentioning

confidence: 99%

Supermetal

Isobe

2019

Phys. Rev. Research

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“…This behavior is linked to an additional symmetry 9 that arises exactly at the monkey saddle, and is a combination of time-reversal transformation (ε, p) → (−ε, −p) plus a particle-hole transformation ψ † ⇌ ψ. This symmetry is present only for odd saddles with ξ(−p) = −ξ(p) and is absent for even saddles that have a dispersion that is invariant under spatial inversion.…”

Section: Rg Flow At the Monkey Saddlementioning

confidence: 99%

Electrons at the monkey saddle: A multicritical Lifshitz point

2017

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We consider 2D interacting electrons at a monkey saddle with dispersion ∝ p 3x − 3pxp 2 y . Such a dispersion naturally arises at the multicritical Lifshitz point when three van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior Em ∝ (Bm) 3 2 and related oscillations in thermodynamic and transport properties, such as de Haas-van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the non-interacting electron fixed point is unstable to interactions under the renormalization group flow, developing either a superconducting instability or non-Fermi liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the K and K ′ points, exhibits an interplay of competing manybody instabilities, namely s-wave superconductivity, ferromagnetism, and spin-and charge-density wave. PACS numbers:arXiv:1606.04950v1 [cond-mat.str-el]

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“…15 In cases where the Fermi surface is singular there are other relevant interactions whose self contractions would vanish [49] algebraically.…”

Section: Fermi Liquid With Broken Rotational Invariancementioning

confidence: 99%

Symmetry realization via a dynamical inverse Higgs mechanism

Rothstein

Shrivastava

2018

J. High Energ. Phys.

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Abstract:The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizing the results for Vishwanath and Wantanabe.

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Wilsonian effective field theory of two-dimensional Van Hove singularities

Cited by 7 publications

References 25 publications

Supermetal

Supermetal

Electrons at the monkey saddle: A multicritical Lifshitz point

Symmetry realization via a dynamical inverse Higgs mechanism

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