Title: Directed-Loop Quantum Monte Carlo Method for Retarded Interactions,
Abstract: The directed-loop quantum Monte Carlo method is generalized to the case of
retarded interactions. Using the path integral, fermion-boson or spin-boson
models are mapped to actions with retarded interactions by analytically
integrating out the bosons. This yields an exact algorithm that combines the
highly-efficient loop updates available in the stochastic series expansion
representation with the advantages of avoiding a direct sampling of the bosons.
The application to electron-phonon models reveals that the method overcomes the
previously detrimental issues of long autocorrelation times and exponentially
decreasing acceptance rates. For example, the resulting dramatic speedup allows
us to investigate the Peierls quantum phase transition on chains of up to
$1282$ sites.