Mitra, S and Hegde, P and Schmidt, C (2022) New way to resum the lattice QCD Taylor series equation of state at finite chemical potential. In: Physical Review D, 106 (3).
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Abstract
Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential μB 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. Recently, a way to resum the contribution of the first N charge density correlation functions D1,...,DN to the Taylor series to all orders in μB was proposed in [Phys. Rev. Lett. 128, 022001 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.022001]. 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 N and μB. 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 M, 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, here we present it for the simpler case of a finite isospin chemical potential μI 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.
| Item Type: | Journal Article |
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| Publication: | Physical Review D |
| Publisher: | American Physical Society |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 14 Sep 2022 09:35 |
| Last Modified: | 14 Sep 2022 09:35 |
| URI: | https://eprints.iisc.ac.in/id/eprint/76445 |
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