Introduction

Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

Frustrated quantum spin systems contain rich physical structures of nontrivial quantum states and phase transitions. The origin of frustration can be a geometric structure or a long-range interaction. The farther spin interactions than the nearest sites stem from a coupling with other degrees of freedom in many realistic materials. Among them, the spin-lattice interaction has a large contribution for the effective spin interaction, and the spin-Peierls system, as a good example, has caught the attention for a long time theoretically and experimentally. At the spin-Peierls transition point, the long-range order of singlet pairs takes place, which entirely results from the quantum nature of the spin degrees of freedom. The analysis of this system and transition will bring understanding of the role of lattice degrees of freedom and nontrivial frustrated spin systems in condensed matter physics. However, the conventional quantum Monte Carlo method cannot calculate the spin-Peierls systems efficiently. In this thesis, we will develop a general improvement of the Markov chain Monte Carlo method, a novel quantum Monte Carlo method for the nonconserved particles, and the quantum Monte Carlo level spectroscopy. Utilizing these new techniques, we will precisely calculate the phase transitions and show the phase diagram of the XXZ spin-Peierls chain, the multi chain, and the two-dimensional spin-Peierls systems for the first time.

Keywords

Frustrated quantum spin system Spin-Peierls system Quantum Monte Carlo method Spin liquid 

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© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of PhysicsBoston UniversityBostonUSA

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