Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
Jürgen Schnack, Johannes Richter, Robin Steinigeweg
Abstract
The authors investigate approximations of the partition function that can be used for large systems where an exact evaluation is impossible. These methods rest on the observation that traces can be replaced by expectation values with respect to a single random vector for not too small temperatures. At low temperatures, where single vectors produce strongly fluctuating approximations, a proper average over many random vectors yields quasi exact results.
Topics & Concepts
MathematicsLanczos resamplingApplied mathematicsSimple (philosophy)Lanczos algorithmFunction (biology)AlgorithmExact solutions in general relativityPartition function (quantum field theory)Multivariate random variablePartition (number theory)Random variableStatistical physicsProbability density functionMathematical analysisCalculus (dental)Random noiseMinificationUnit vectorLimit (mathematics)Quantum many-body systemsAdvanced Thermodynamics and Statistical MechanicsTheoretical and Computational Physics