Conformal invariance in three dimensional percolation

Gori, Giacomo; Trombettoni, Andrea

doi:10.1088/1742-5468/2015/07/p07014

Cited by 18 publications

(18 citation statements)

References 52 publications

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“…This symmetry, conjectured long ago [42], has in two dimensions far-reaching consequences [40,41], as it fixes completely the universality class. Numerical studies both in two and three dimensions gave a clear evidence of the presence of CS for short-range models [43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 91%

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

et al. 2016

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We deal with the problem of studying the symmetries and the effective theories of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and interesting, where to investigate these questions, we focus on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent α. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. Two critical lines are found, occurring respectively at a positive and a negative chemical potential. Focusing first on the critical line at positive chemical potential, by means of a renormalization group approach we derive its effective theory close to criticality. Our main result is that the effective action is the sum of two terms: a Dirac action SD, found in the short-range Ising universality class, and an "anomalous" CS breaking term SAN. While SD originates from low-energy excitations in the spectrum, SAN originates from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality SAN flows to zero for α > 2, while for α < 2 it dominates and determines the breakdown of the CS. Out of criticality SAN breaks, in the considered approximation, the effective Lorentz invariance (ELI) for every finite α. As α increases such ELI breakdown becomes less and less pronounced and in the short-range limit α → ∞ the ELI is restored. In order to test the validity of the determined effective theory, we compared the two-fermion static correlation functions and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. These results explain two observed features characteristic of long-range models, the hybrid decay of static correlation functions within gapped phases and the area-law violation for the von Neumann entropy. The proposed scenario is expected to hold in other longrange models displaying quasiparticle excitations in ballistic regime. From the effective theory one can also see that new phases emerge for α < 1. Finally we show that at every finite α the critical exponents, defined as for the short-range (α → ∞) model, are not altered. This also shows that the long-range paired Kitaev chain provides an example of a long-range model in which the value of α where the CS is broken does not coincide with the value at which the critical exponents start to differ from the ones of the corresponding shortrange model. At variance, for the second critical line, having negative chemical potential, only SAN (SD) is present for 1 < α < 2 (for α > 2). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change where CS is broken.

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Section: Introductionmentioning

confidence: 91%

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

et al. 2016

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“…1 We would also like to point out a related lattice study of conformal invariance in 3d percolation [4].…”

Section: E Heuristic Optimization Of Boundary Conditions 25mentioning

confidence: 99%

“…In infinite volume vector operators would have zero 1pt functions, but in finite volume with appropriate boundary conditions they can be nonzero. In our case we will have 4) with no dependence on x 2 due to the translation invariance in that direction. The scaling of this observable with L will be determined by the smaller of the two dimensions ∆ V , ∆ ∂T = ∆ T + 1:…”

Section: )mentioning

confidence: 99%

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A structural test for the conformal invariance of the critical 3d Ising model

Meneses

Rychkov

et al. 2019

J. High Energ. Phys.

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How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -a non-conserved vector operator of dimension exactly (d − 1), whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound ∆ V > 5.0 on the scaling dimension of the lowest virial current candidate V , well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model. E. Heuristic optimization of boundary conditions 251 We would also like to point out a related lattice study of conformal invariance in 3d percolation [4].

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“…Any results could be compared to predictions coming from the 6 − expansion or Monte Carlo methods [107][108][109].…”

Section: Jhep10(2017)201mentioning

confidence: 99%

The ABC (in any D) of logarithmic CFT

Hogervorst

Paulos

Vichi

2017

J. High Energ. Phys.

103

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Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is modelindependent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

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Conformal invariance in three dimensional percolation

Cited by 18 publications

References 52 publications

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

A structural test for the conformal invariance of the critical 3d Ising model

The ABC (in any D) of logarithmic CFT

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