Efficient computations of continuous action densities of states for lattice models

Biagio Lucini, Olmo Francesconi, Markus Holzmann, David Lancaster, Antonio Rago

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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.

Original languageEnglish
Article number012052
Book seriesJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 28. Mar 2022
Event32nd IUPAP Conference in Computational Physics, CCP 2021 - Coventry, Virtual, United Kingdom
Duration: 2. Aug 20215. Aug 2021


Conference32nd IUPAP Conference in Computational Physics, CCP 2021
Country/TerritoryUnited Kingdom
CityCoventry, Virtual


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