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Springer theses

Monte Carlo Method for Spin-Peierls Systems

Hidemaro Suwa

Published Nov 5, 2013• 0 citations
Publisher
DOI
10.1007/978-4-431-54517-0_3

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•Jan 1, 2019•0 citations
We provide a concrete and systematic connection between the statistical physics of the Ising ferromagnet on a Cayley tree, and the study of memory in exponentially expanding spaces. Memory turns out to be a clear signal of the `Bethe-Peierls' phase transition, and the average of memory divided by its standard deviation provides a clear signal of the `spin-glass' transition temperature. Numerical Monte Carlo simulations are used to make transparent the existence of the two different transition temperatures. The quantities used to spot the phase transitions with Monte Carlo could be useful when studying other systems where analytical methods don't work.
This work deals with the development and application of novel quantum Monte Carlo methods to simulate fermion-boson models. Our developments are based on the path-integral formalism, where the bosonic degrees of freedom are integrated out exactly to obtain a retarded fermionic interaction. We give an overview of three methods that can be used to simulate retarded interactions. In particular, we develop a novel quantum Monte Carlo method with global directed-loop updates that solves the autocorrelation problem of previous approaches and scales linearly with system size. We demonstrate its efficiency for the Peierls transition in the Holstein model and discuss extensions to other fermion-boson models as well as spin-boson models. Furthermore, we show how with the help of generating functionals bosonic observables can be recovered directly from the Monte Carlo configurations. This includes estimators for the boson propagator, the fidelity susceptibility, and the specific heat of the Holstein model. The algorithmic developments of this work allow us to study the specific heat of the spinless Holstein model covering its entire parameter range. Its key features are explained from the single-particle spectral functions of electrons and phonons. In the adiabatic limit, the spectral properties are calculated exactly as a function of temperature using a classical Monte Carlo method and compared to results for the Su-Schrieffer-Heeger model.