The Logarithmic Linear Relaxation (LLR) algorithm is an efficient method for computing densities of states for systems with a continuous spectrum. A key feature of this method is exponential error reduction, which allows us to evaluate the density of states of a system over hundreds of thousands of orders of magnitude with a fixed level of relative accuracy. As a consequence of exponential error reduction, the LLR method provides a robust alternative to traditional Monte Carlo calculations in cases in which states suppressed by the Boltzmann weight play nevertheless a relevant role, e.g., as transition regions between dominant configuration sets. After reviewing the algorithm, we will show an application in U(1) Lattice Gauge Theory that has enabled us to obtain the most accurate estimate of the critical coupling with modest computational resources, defeating exponential tunneling times between metastable vacua. As a further showcase, we will then present an application of the LLR method to the decorrelation of the topological charge in SU(3) Lattice Gauge Theory near the continuum limit. Finally, we will review in general applications of the LLR algorithm to systems affected by a strong sign problem and discuss the case of the Bose gas at finite chemical potential.
|Bogserie||Journal of Physics: Conference Series|
|Status||Udgivet - 28. mar. 2022|
|Begivenhed||32nd IUPAP Conference in Computational Physics, CCP 2021 - Coventry, Virtual, Storbritannien|
Varighed: 2. aug. 2021 → 5. aug. 2021
|Konference||32nd IUPAP Conference in Computational Physics, CCP 2021|
|Periode||02/08/2021 → 05/08/2021|
Bibliografisk noteFunding Information:
This work has been partially supported by the ANR project ANR-15-IDEX-02e. The work of BL is supported in part by the Royal Society Wolfson Research Merit Award WM170010 and by the Leverhulme Foundation Research Fellowship RF-2020-461\9. BL received funding also from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 813942. AR is supported by the STFC Consolidated Grant ST/P000479/1. Numerical simulations have been performed on the Swansea SUNBIRD system, provided by the Supercomputing Wales project, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government, and on the HPC facilities at the HPCC centre of the University of Plymouth.
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