Overview

In this thesis, novel Monte Carlo methods for precisely calculating the critical phenomena of the effectively frustrated quantum spin system are developed and applied to the critical phenomena of the spin-Peierls systems. Three significant methods are introduced for the first time: a new optimization algorithm of the Markov chain transition kernel based on the geometric weight-allocation approach, the extension of the worm (directed-loop) algorithm to nonconserved particles, and the combination with the level spectroscopy. Utilizing these methods, the phase diagram of the one-dimensional XXZ spin-Peierls system is elucidated. Furthermore, the multi-chain and two-dimensional spin-Peierls systems with interchain lattice interaction are investigated. The unbiased simulation shows that the interesting quantum phase transition between the 1D-like liquid phase and the macroscopically-degenerated dimer phase occurs on the fully-frustrated parameter line that separates the doubly-degenerated dimer phases in the two-dimensional phase diagram. The spin-phonon interaction in the spin-Peierls system introduces the spin frustration, which usually hinders the quantum Monte Carlo analysis, owing to the notorious negative sign problem. In this thesis, the author has succeeded in precisely calculating the critical phenomena of the effectively frustrated quantum spin system by means of the quantum Monte Carlo method without the negative sign.

Full Product Details

Author:   Hidemaro Suwa
Publisher:   Springer Verlag, Japan
Imprint:   Springer Verlag, Japan
Edition:   Softcover reprint of the original 1st ed. 2014
Dimensions:   Width: 15.50cm , Height: 0.80cm , Length: 23.50cm
Weight:   2.234kg
ISBN:  

9784431563679

ISBN 10:   4431563679
Pages:   126
Publication Date:   23 August 2016
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Introduction.- Geometric Allocation Approach in Markov Chain Monte Carlo.- Monte Carlo Method for Spin-Peierls Systems.- Quantum Monte Carlo Level Spectroscopy.- XXZ Spin-Peierls Chain.- Multi-chain Spin-Peierls Systems.- Summary.

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