A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential

Mitra S, Hegde P, Schmidt-Sonntag C (2022)
arXiv:2205.08517.

Preprint | Englisch
 
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Autor*in
Mitra, Sabarnya; Hegde, Prasad; Schmidt-Sonntag, ChristianUniBi
Abstract / Bemerkung
Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential μB\mu_BμB​ is a well-known method to bypass the Sign Problem of Lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients, various alternative expansion schemes as well as resummation techniques have been suggested to extend the Taylor series to larger values of μB\mu_BμB​. Recently, a way to resum the contribution of the first NNN charge density correlation functions D1,…,DND_1,\dots,D_ND1​,…,DN​ to the Taylor series to all orders in μB\mu_BμB​ was proposed in Phys. Rev. Lett. 128, 2, 022001 (2022). The resummation takes the form of an exponential factor. Since the correlation functions are calculated stochastically, the exponential factor contains a bias which can be significant for large NNN and μB\mu_BμB​. In this paper, we present a new method to calculate the QCD equation of state based on the well-known cumulant expansion from statistics. By truncating the expansion at a maximum order MMM, we end up with only finite products of the correlation functions which can be evaluated in an unbiased manner. Although our formalism is also applicable for μB≠0\mu_B\ne0μB​=0, here we present it for the simpler case of a finite isospin chemical potential μI\mu_IμI​ for which there is no Sign Problem. We present and compare results for the pressure and the isospin density obtained using Taylor expansion, exponential resummation and cumulant expansion, and provide evidence that the absence of bias in the latter actually improves the convergence.
Erscheinungsjahr
2022
Zeitschriftentitel
arXiv:2205.08517
Page URI
https://pub.uni-bielefeld.de/record/2963748

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Mitra S, Hegde P, Schmidt-Sonntag C. A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential. arXiv:2205.08517. 2022.
Mitra, S., Hegde, P., & Schmidt-Sonntag, C. (2022). A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential. arXiv:2205.08517
Mitra, S., Hegde, P., and Schmidt-Sonntag, C. (2022). A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential. arXiv:2205.08517.
Mitra, S., Hegde, P., & Schmidt-Sonntag, C., 2022. A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential. arXiv:2205.08517.
S. Mitra, P. Hegde, and C. Schmidt-Sonntag, “A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential”, arXiv:2205.08517, 2022.
Mitra, S., Hegde, P., Schmidt-Sonntag, C.: A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential. arXiv:2205.08517. (2022).
Mitra, Sabarnya, Hegde, Prasad, and Schmidt-Sonntag, Christian. “A New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential”. arXiv:2205.08517 (2022).

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