Numerical study of quantum spin systems with spatial structure

Abstract

The Hamiltonian function for the ground state of the S = 1/2 bilayer J(sub 1)-J(sub 2) model has been studied by means of the dimer expansion method. The phase boundary between the spin-gap phase and the magnetically ordered phase was determined from the poles of the biased Pade approximations for the susceptibility and the energy gap. The Hamiltonian function for the one-dimensional S = 1/2 Heisenberg model with dimerization and quadrumerization has been studied using the numerical exact diagonalization method of finite size systems. The obtained ground state phase diagram in the isotropic case was shown in a figure. The Hamiltonian function for the low temperature magnetization process of the spin-1/2 ferromagnetic-antiferromagnetic Heisenberg chain has been studied. The quantum Monte Carlo simulation was performed and compared with the boson approximation. It was found that the boson approximation gives a semi-quantitative description of the low temperature magnetization curve for low field regime and nearly saturated regime.

S=1/2で2層J(sub 1)-J(sub 2)模型の基底状態に対するハミルトン関数を2量体展開法により研究した。スピンギャップ相と磁気的秩序相の間の相境界を磁化率およびエネルギーギャップに対する偏奇パデ近似の極から決定した。2量化と4量化を有する1次元S=1/2ハイゼンベルク模型に対するハミルトン関数を、有限サイズ系の数値的厳密対角化法を用いて研究した。等方性ハイゼンベルク鎖の事例で求めた基底状態の状態図を図示した。スピン-1/2強磁性-反強磁性ハイゼンベルク鎖の低温磁化過程に対するハミルトン関数を研究した。量子モンテカルロ・シミュレーションを行い、ボソン近似と比較した。ボソン近似は、低磁場領域および飽和寸前領域に対して半定量的低温磁化曲線を記述することが分かった。