Kuantum Monte Carlo yönteminin spin sistemlerine genel uygulaması

In this thesis, we mainly study a general Monte Carlo technique for simulating spin models with quantum mechanical interactions either at finite or zero temperatures. From the two dominating simulation techniques the so-called stochastic series expansion method is challenging the other major method path integral quantum Monte Carlo in recent years. The theoretical and technical details of the stochastic series expansion quantum Monte Carlo technique consist of the main body of this thesis. The simulation technique is formulated in a general manner and the technical details are illustrated in the scope of the isotropic spin-half models without external fields for both the ferromagnetic and antiferromagnetic interactions. Complete pseudocodes are given with detailed explanations and benchmark results are compared with exact diagonalization calculations. We briefly mention the ideas of spin systems, critical phenomena, and basics of Monte Carlo that are minimally required for a solid understanding of the simulation technique at the algorithmic level. The simulation technique is applied to two physical systems. The thermal properties of a two-leg spin ladder model with a bond disorder are investigated and interestingly a crossing point is monitored for uniform susceptibility and specific heat, separately. Finally, a three-dimensional system with a disorder is reviewed as evidence of the strength of the simulation technique in exploring the critical and universal properties. The technical details will serve as a concrete background to easily extend the underlying algorithm to include a variety of models.