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arXiv:2303.16719 · Physical review. D/Physical review. D.

Scalar spectral functions from the spectral functional renormalization group

Jan Horak, Friederike Ihssen, Jan Martin Pawlowski, Jonas Wessely, Nicolas Wink

Published Sep 5, 2024• 12 citations
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Abstract

We compute spectral functions in a scalar ϕ 4 -theory in three spacetime dimensions via the spectral functional renormalization group. This approach allows for the direct, manifestly Lorentz covariant computation of correlation functions in Minkowski spacetime, including a physical on-shell renormalization. We present numerical results for the spectral functions of the two- and four-point correlation functions for different values of the coupling parameter. These results agree very well with those obtained from another functional real-time approach, the spectral Dyson-Schwinger equation. Published by the American Physical Society 2024

DOI
10.1103/physrevd.110.056009

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We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable truncation schemes for real-time calculations, as well as the numerical procedure to self-consistently solve the flow equations for the spectral function. Subsequently, we discuss the relations to other perturbative and nonperturbative approaches to calculate spectral functions and present a detailed comparison and benchmark in d=0+1d=0+1d=0+1 dimensions.
Real-time dynamics of the O(4)O(4)O(4) scalar theory within the fRG approach
In this paper, the real-time dynamics of the O(4) O ( 4 ) scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path. The flow equations for the effective action and its n n -point correlation functions are derived in terms of the "classical'' and "quantum’’ fields, and a concise diagrammatic representation is presented. An analytic expression for the flow of the four-point vertex is obtained. Spectral functions with different values of temperature and momentum are obtained. Moreover, we calculate the dynamical critical exponent for the phase transition near the critical temperature in the O(4) O ( 4 ) scalar theory in 3+1 3 + 1 dimensions, and the value is found to be z\simeq 2.023 z ≃ 2.023 .
The Schwinger-Keldysh functional renormalization group developed by Y.-y. Tan [Real-time dynamics of the O ( 4 ) scalar theory within the fRG approach, ] is employed to investigate critical dynamics related to a second-order phase transition. The effective action of model A is expanded to the order of O ( ∂ 2 ) in the derivative expansion for the O ( N ) symmetry. By solving the fixed-point equations of effective potential and wave function, we obtain static and dynamic critical exponents for different values of the spatial dimension d and the field component number N . It is found that one has z ≥ 2 in the whole range of 2 ≤ d ≤ 4 for the case of N = 1 , while in the case of N = 4 , the dynamic critical exponent turns to z < 2 when the dimension approach towards d = 2 . Published by the American Physical Society 2024
A bstract We present first calculations of critical spectral functions of the relaxational Models A, B, and C in the Halperin-Hohenberg classification using a real-time formulation of the functional renormalization group (FRG). We revisit the prediction by Son and Stephanov that the linear coupling of a conserved density to the non-conserved order parameter of Model A gives rise to critical Model-B dynamics. We formulate both 1-loop and 2-loop self-consistent expansion schemes in the 1PI vertex functions as truncations of the effective average action suitable for real-time applications, and analyze in detail how the different critical dynamics are properly incorporated in the framework of the FRG on the closed-time path. We present results for the corresponding critical spectral functions, extract the dynamic critical exponents for Models A, B, and C, in two and three spatial dimensions, respectively, and compare the resulting values with recent results from the literature.