京都大学 / 0048 / 新制・課程博士 / 博士(薬科学) / 甲第18918号 / 薬科博第32号 / 新制||薬||4(附属図書館) / 31869 / 京都大学大学院薬学研究科薬科学専攻 / (主査)教授 松﨑 勝巳, 教授 加藤 博章, 教授 石濱 泰 / 学位規則第4条第1項該当 / Doctor of Pharmaceutical Sciences / Kyoto University / DGAM

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<p>In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.</p> / Master of Science (MSc)