Quantum statistical monte carlo methods and applications to spin systems

Masuo Suzuki

J. W. Lyklema

An exact Monte Carlo method for calculating thermodynamic properties of quantum spin systems is described. Results for one-dimensional ferromagnetic and antiferromagnetic systems and for three-dimensional ferromagnetic systems show that the method can be used to study quantum spin systems as extensively as classical spin systems are studied with conventional Monte Carlo methods.

Yutaka Okabe, Ishizuka Jun-ichi, 岡部 豊 +1 more

Robert Achleitner

This thesis work deals with Monte Carlo (MC) simulations with the focus on quantum mechanical systems. I start with an introduction about Monte-Carlo methods in general and their application to the classical Ising model. The second, most important part deals with the problem in quantum mechanics, and presents a possible simulation method, the Stochastic Series Expansion (SSE). I give an introduction about the idea behind that method and give some results obtained for simulations for finite spin chains. All programming was performed in FORTRAN.

Sakaguchi Toshifumi

Shinji Kadowaki, Akira Ueda

A simple Monte Carlo method1) which was shown to be applicable to finite spin-systems of rather large spin size ragardless of dimensionality of the system is applied to the spin-1/2 isotropic Heisenberg ferromagnetic system on the square lattice of spin size 10 × 10, 20 × 20 and 30 × 30. Rather accurate values are obtained for thermodynamic quantities for temperature down to k B T / J =0.01. The accuracy and efficiency of the MC method are discussed in detail in comparison with the other works.