3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory

Lao, Bing-Xin; Rychkov, Slava

doi:10.21468/scipostphys.15.6.243

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…In addition, we find that our results for both these and the λ n IJ CϵC coefficients have smaller errors. We note that our new value of the λ 0 T ϵT OPE coefficient still satisfies the bounds set in [69] (|λ 0 T ϵT | ≃ 0.958(7) ≤ 0.981(2)), and is close to but somewhat larger than the value λ 0 T ϵT ≃ 0.9162 (73) computed in [70] using the fuzzy sphere regularization approach [70][71][72][73]. It will be interesting to study how this OPE coefficient is affected by subleading 1/N corrections in the fuzzy sphere method.…”

Section: Jhep05(2024)299supporting

confidence: 68%

Improving the five-point bootstrap

Poland,

Prilepina,

Tadić

2024

J. High Energ. Phys.

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We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

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Section: Jhep05(2024)299supporting

confidence: 68%

Improving the five-point bootstrap

Poland,

Prilepina,

Tadić

2024

J. High Energ. Phys.

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“…Secondly, it allows for the direct extraction of various data of the CFTs, including numerous scaling dimensions of conformal primary operators [1,10], operator product expansion coefficients [8], and four-point correlators [9]. For instance, scaling dimensions can be computed directly from excitation energies of the system, and their accuracy can be further improved using conformal perturbation [12]. Thirdly, the fuzzy sphere scheme is applicable to a variety of 3D CFTs, including Ising [1], O(N) Wilson-Fisher, SO(5) deconfined phase transition [10], critical gauge theories [10], and defect CFTs [11].…”

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

Hofmann,

Goth,

Zhu

et al. 2024

SciPost Phys. Core

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We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional SU(2) layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

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Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods

2024

J. High Energ. Phys.

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As a simple lattice model that exhibits a phase transition, the Ising model plays a fundamental role in statistical and condensed matter physics. The Ising transition is realized by physical systems, such as the liquid-vapor transition. Its continuum limit also furnishes a basic example of interacting quantum field theories and universality classes. Motivated by a recent hybrid bootstrap study of the quantum quartic oscillator, we revisit the conformal bootstrap approach to the 3D Ising model at criticality, without resorting to positivity constraints. We use at most 10 nonperturbative crossing constraints at low derivatives from the Taylor expansion around a crossing symmetric point. The high-lying contributions are approximated by simple analytic formulae deduced from the lightcone singularity structure. Surprisingly, the low-lying properties are determined to good accuracy by this computationally very cheap approach. For instance, the results for the two relevant scaling dimensions (∆σ, ∆ϵ) ≈ (0.518153, 1.41278) are close to the most precise rigorous bounds obtained at a much higher computational cost.

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3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory

Cited by 6 publications

References 21 publications

Improving the five-point bootstrap

Improving the five-point bootstrap

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods

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