Theoretical and Numerical Study of Many-Body Interaction and Quantum Phase Transition in Low-Dimensional Magnets

1)用新的积分方程对XXX模型进行高温展开用有限集团方法对一维Heisenberg模型的比热、磁化率等热力学量进行了24阶的高温展开。另一方面，据信通过贝特膨胀法的高温膨胀是困难的。但我们成功地扩展到100阶，使用新的热力学贝特方程。我们采用Pade近似，并与量子转移矩阵方法的数值结果进行了比较。2）Hubbard模型的Bethe近似方程与高温展开式的比较热力学Bethe近似方程有无穷多个未知函数。对非线性积分方程作了截断处理，并用牛顿法求解。热力学量一般用巨势的微分表示。然后，我们必须求解线性积分方程，以获得热力学量。但是这个方程可以用牛顿法中的同样方法来完成。一维各向同性XY模型的空性形成概率我们用数值和解析方法研究了一维XY模型的空性形成概率，它是一维各向同性XY模型的多点核函数之一

1) High temperature expansion of XXX model by new integral equationHigh temperature expansion of thermodynamic quantities such as specific heat and magnetic susceptibility for one-dimensional Heisenberg model has been done up to 24-th order using finite cluster method. On the other hand high temperature expansion by Bethe ansatz method was believed to be difficult. But we succeeded to expand to 100th order using new thermodynamic Bethe ansatz equation. We apply Pade approximation and compared with the numerical results of quantum transfer matrix method.2) Comparison of Bethe ansatz equation with high-temperature expansion for Hubbard modelThermodynamic Bethe ansatz equation has infinite number of unknown functions. We made cut off and used Newton's method to solve non-linear integral equation. Generally speaking thermodynamic quantities are expressed by the differentiation of grand potential. Then we must solve linear integral equation to get thermodynamic quantities. But this equation can be done in the same method in Newton's method. Only by one time linear operation we can get first order thermodynamic quantities such as energy, entropy, magnetization and particle density.3) Emptiness formation probability of one-dimensional isotropic XY modelWe investigated the emptiness formation probability which is one of many points corellation functions for one-dimensional XY model using numerical and analytical methods