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This book provides a comprehensive treatment of the two fundamental aspects of a solid that determine its physical properties: lattice structure and atomic vibrations (phonons). The elements of group theory are extensively developed and used as a tool to show how the symmetry of a solid and the vibrations of the atoms in the solid lead to the physical properties of the material. The uses of different types of spectroscopy techniques that elucidate the lattice structure of a solid and the normal vibrational modes of the atoms in the solid are described. The interaction of light with solids (opt

Lattice dynamics. --- Phonons. --- Symmetry (Physics) --- Optical spectroscopy. --- Solid state physics. --- Physics --- Solids --- Spectroscopy, Optical --- Visible spectroscopy --- Spectrum analysis --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Conservation laws (Physics) --- Quasiparticles (Physics) --- Lattice dynamics --- Dynamics, Lattice --- Crystal lattices --- Phonons --- Group theory --- Solid state physics

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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.

Monte Carlo method. --- Markov processes. --- Phonons. --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Physics. --- Computer simulation. --- Quantum physics. --- Quantum computers. --- Spintronics. --- Applied mathematics. --- Engineering mathematics. --- Quantum Physics. --- Numerical and Computational Physics. --- Quantum Information Technology, Spintronics. --- Simulation and Modeling. --- Appl.Mathematics/Computational Methods of Engineering. --- Quasiparticles (Physics) --- Lattice dynamics --- Stochastic processes --- Games of chance (Mathematics) --- Mathematical models --- Numerical analysis --- Numerical calculations --- Quantum theory. --- Numerical and Computational Physics, Simulation. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Simulation methods --- Model-integrated computing --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Mathematics --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Computers --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics