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Free energy of the self-interacting relativistic lattice Bose gas at finite density

Olmo Francesconi, Markus Holzmann, Biagio Lucini Orcid Logo, Antonio Rago

Physical Review D, Volume: 101, Issue: 1

Swansea University Authors: Olmo Francesconi, Biagio Lucini Orcid Logo

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Abstract

The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the linear logarithmic relaxation (LLR) algorithm, we extract the generalized density of states, which is defined in terms of the imaginary...

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Published in: Physical Review D
ISSN: 2470-0010 2470-0029
Published: American Physical Society (APS) 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa53252
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Abstract: The density of state approach has recently been proposed as a potential route to circumvent the sign problem in systems at finite density. In this study, using the linear logarithmic relaxation (LLR) algorithm, we extract the generalized density of states, which is defined in terms of the imaginary part of the action, for the self-interacting relativistic lattice Bose gas at finite density. After discussing the implementation and testing the reliability of our approach, we focus on the determination of the free energy difference between the full system and its phase quenched counterpart. Using a set of lattices ranging from 44 to 164, we show that in the low density phase, this overlap free energy can be reliably extrapolated to the thermodynamic limit. The numerical precision we obtain with the LLR method allows us to determine with sufficient accuracy the expectation value of the phase factor, which is used in the calculation of the overlap free energy, down to values of Oð10−480Þ. When phase factor measurements are extended to the dense phase, a change of behavior of the overlap free energy is clearly visible as the chemical potential crosses a critical value. Using fits inspired by the approximate validity of mean-field theory, which is confirmed by our simulations, we extract the critical chemical potential as the nonanalyticity point in the overlap free energy, obtaining a value that is in agreement with other determinations. Implications of our findings and potential improvements of our methodology are also discussed.
College: Faculty of Science and Engineering
Funders: ANR, Royal Society, ERDF
Issue: 1