TY - BOOK ID - 14220647 TI - Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems PY - 2014 SN - 4431545166 4431545174 PB - Tokyo : Springer Japan : Imprint: Springer, DB - UniCat KW - Monte Carlo method. KW - Markov processes. KW - Phonons. KW - Analysis, Markov KW - Chains, Markov KW - Markoff processes KW - Markov analysis KW - Markov chains KW - Markov models KW - Models, Markov KW - Processes, Markov KW - Artificial sampling KW - Model sampling KW - Monte Carlo simulation KW - Monte Carlo simulation method KW - Stochastic sampling KW - Physics. KW - Computer simulation. KW - Quantum physics. KW - Quantum computers. KW - Spintronics. KW - Applied mathematics. KW - Engineering mathematics. KW - Quantum Physics. KW - Numerical and Computational Physics. KW - Quantum Information Technology, Spintronics. KW - Simulation and Modeling. KW - Appl.Mathematics/Computational Methods of Engineering. KW - Quasiparticles (Physics) KW - Lattice dynamics KW - Stochastic processes KW - Games of chance (Mathematics) KW - Mathematical models KW - Numerical analysis KW - Numerical calculations KW - Quantum theory. KW - Numerical and Computational Physics, Simulation. KW - Mathematical and Computational Engineering. KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Computer modeling KW - Computer models KW - Modeling, Computer KW - Models, Computer KW - Simulation, Computer KW - Electromechanical analogies KW - Simulation methods KW - Model-integrated computing KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Physics KW - Mechanics KW - Thermodynamics KW - Mathematics KW - Fluxtronics KW - Magnetoelectronics KW - Spin electronics KW - Spinelectronics KW - Microelectronics KW - Nanotechnology KW - Computers KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14220647 AB - 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. ER -