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The Logarithmic Linear Relaxation (LLR) algorithm is an efficient method forcomputing densities of states for systems with a continuous spectrum. A keyfeature of this method is exponential error reduction, which allows us toevaluate the density of states of a system over hundreds of thousands of ordersof magnitude with a fixed level of relative accuracy. As a consequence ofexponential error reduction, the LLR method provides a robust alternative totraditional Monte Carlo calculations in cases in which states suppressed by theBoltzmann weight play nevertheless a relevant role, e.g., as transition regionsbetween dominant configuration sets. After reviewing the algorithm, we willshow an application in U(1) Lattice Gauge Theory that has enabled us to obtainthe most accurate estimate of the critical coupling with modest computationalresources, defeating exponential tunneling times between metastable vacua. As afurther showcase, we will then present an application of the LLR method to thedecorrelation of the topological charge in SU(3) Lattice Gauge Theory near thecontinuum limit. Finally, we will review in general applications of the LLRalgorithm to systems affected by a strong sign problem and discuss the case ofthe Bose gas at finite chemical potential.

Efficient computations of continuous action densities of states for lattice models