所谓电子关联体系，即考虑了电子和电子之间存在相互作用的体系，这样的体系无疑更接近于真实材料，但也更为难以进行理论研究。在已有的探究中发现，一些电子关联材料具有非常丰富的磁性和输运特性，并存在着奇异的量子相变现象，这对于凝聚态物理基础理论和应用的研究意义重大。基于描述强关联体系的Hubbard模型和重费米子体系的PAM（Periodic Anderson Model）模型，本文探究了在掺杂和无序效应的作用下，强关联电子体系中电子的局域化行为模式，以及体系中磁关联的形成。 论文的第一章，我们从紧束缚(Tight Binding)模型出发，简单介绍了能带理论的发展，以及强关联电子体系的发现过程。并讨论了Hubbard 模型中的Mott 绝缘体形成机制以及PAM模型中Kondo 单重态和磁有序的竞争。第二章中，介绍了本文中用来处理强关联电子体系模型的两种量子蒙特卡罗算法，有限温行列式量子蒙特卡罗方法（DQMC）和基态约束路径量子蒙特卡罗方法（CPMC）。 在第三章中，我们使用DQMC方法，研究了六角晶格上的二维Dirac 电子体系，该体系的费米能级具有线性消失的态密度，这样特殊的能带结构，预示着这种材料具有丰富的电学特性。因为我们研究的体系是基于半满电子填充的排斥哈伯德模型，可以不考率DQMC 方法中的符号问题。在本章的工作中，我们研究了多体关联驱动与无序效应驱动的电子局域化，以及这两种机制的相互作用过程。通过计算，我们发现了一个新的由无序引发的非磁性绝缘相，该相出现在半金属到莫特绝缘体转变的零温量子临界点区域。在这个无序绝缘相区内，存在着从无能隙类Anderson绝缘体到有能隙类Mott 绝缘体的过渡边界。 应力应变作为调控电子特性的另一种可能性机制，也是一个非常值得研究的问题。在论文的第四章的工作中，我们使用了DQMC，对施加了单轴应变的单层六角晶格上的半金属-模特绝缘体相变过程，进行了数值分析计算。在第四章的研究内容中，我们先计算了与温度有关的用于表征电子传输特性的直流导电率。着重讨论了多体关联驱动电子局域化机制与应力形变导致的电子局域化机制之间的相互作用效应。然后，我们还通过CPMC方法计算了反铁磁结构因子（AF），描述体系的磁性性质在应变下的变化。我们的计算结果表明，在应变的作用下，体系的金属性行为会受到抑制，在相互作用影响下会更早的进入绝缘相区；另外，应变的作用，可以保护反铁磁长程序。根据我们的计算结果，我们得到了一个在应变和相互作用竞争机制下，金属绝缘转变的拓展区域以及新的反铁磁相区。 近藤（Kondo）和周期性安德森模型（PAM）定性的描述了局域化磁矩和导带耦合作用的系统特征，常常被用来研究关联电子体系中重费米子材料的物理特性。尤其是，当局域磁矩和金属带电子之间的交换相互作用$J$或者杂化强度$V$很大的时候，会形成Kondo 单重态结构，并且破坏材料的磁性。另一方面，当$J$ 和$V$比较小时，在极限情况下，局域磁矩没有被破坏，以导带中的电子为相互作用媒介，会触发磁矩之间形成长程序，通常情况下就是反铁磁长程序（AF）。在近藤（Kondo）模型中，磁矩是由局域化自旋电子形成的。而Nozi\'eres'提出了一个设想，当在费米面Kondo 温度下有效的导带电子数不足以形成完整的近藤屏蔽时，会出现什么现象呢？在大量的文献中，已经有人研究了产生这种所谓“exhaustion”效应的温度尺度，以及形成重费米液体的“关联”温度和Kondo温度的关系。在第五章的工作中，我们研究了这样一个PAM模型，体系中的一些导带电子被剔除掉了，由于体系是半满填充的，这避开了量子蒙特卡洛算法中模拟过程会遇到的符号问题，并且可以使用量子蒙特卡洛算法模拟低温环境，以此得到较为稳定的体系Kondo 单重态和磁序结构。然后，在第五章的工作中，我们将重点放在与之前Nozi\'eres'设想中，“exhaustion” 效应导致的物理现象中一个稍微不同的方面：研究了导带电子浓度的减少对Kondo单重态- 反铁磁转变的临界杂化强度V的影响。

In consideration of the interaction between electrons and electrons, the system is electronic correlated. Such a model is more difficult to solve analytically but more like a real material. It has been found that some correlated materials have very rich magnetic and electronic transport properties, and novel quantum phase transition phenomena is also observed. The correlated material gives a rise to the fundamental theory exploration and application of the condensed matter physics. Based on the Hubbard model which used to describe the strongly correlated system，and the Periodic Anderson Model (PAM) which capture the basic properties of heavy fermion materials, in this paper, the localized behavior of electrons and the formation of magnetic correlations are investigated under the effects of doping and disorder effect. In the first Chapter of this paper, we start from the basic idea of tight-binding model and briefly introduced the band theory. Then, we comes to the discover of correlated materials. Hubbard model and PAM are widely used to study correlated materials. So that we also briefly introduced the Mott insulator and the competition between singlet formation and magnetic order to help us understand the underlying physics described by Hubbard model and PAM. While for the Chapter 2, two Quantum Monte Carlo methods are discussed in this part. One is the finite temperature Determinant Quantum Monte Carlo method (DQMC) and the other is the ground state Constrained Path quantum Monte Carlo method (CPMC). In Chapter 3, using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. Since our simulations are based on the half-filled repulsive Hubbard model, the system is sign problem free. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed. Motivated by the possibility of strain tuning effect in electronic properties, we numerically study the semi-metal - Mott insulator transition process on the uniaxial honeycomb lattice using the Determinant Quantum Monte Carlo method. In Chapter 4, we use the temperature dependent DC conductivity to characterize electronic transport properties. And we captured the interplay between localization of electronic states driven by many-body correlations and stress effect in a two-dimensional system featuring vanishing density of states at the Fermi level. The antiferromagnetic structure factor AF is also calculated by CPMC method to describe the behavior of magnetic properties under stress. Our data suggest that metallic is suppressed with the presence of strain, and the system will turn into insulator earlier as strain applied. As for AF order, strain help preserve the magnetic order. Thus, according to our simulation results, there exists a new region in the MIT phase diagram that generated by the competition between interactions and strain, and also a novel antiferromagnetic region comes to our eyes. The Kondo and Periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling $J$ or hybridization $V$ between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small $J$ or $V$, limit, the moments survive, and the conduction electrons mediate an effective interaction which can trigger long range, often antiferromagnetic (AF), order. In the case of the Kondo model, where the moments are described by local spins, Nozi\`eres' considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting `exhaustion' problem, and how the `coherence temperature' where a heavy Fermi liquid forms is related to the Kondo temperature. In Chapter 4, we study a version of the PAM in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low temperature Quantum Monte Carlo (QMC) simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical V for the singlet-AF transition.