Quantum Phase Transitions in Condensed Matter

将对量子相位进行理论研究 过渡，即phemonena，其中基态的一个 多体系统的定性变化，因为某些控制参数是 在零温度下变化。 其中包括从金属 作为相互作用强度、随机性或 磁序随空穴密度的变化， 或者说微观耦合， 金属掺杂到超导体。 所有这些问题 一般没有明显的小参数 以进行清晰的理论计算。 这将在 多种方式：通过与低维类似物合作， 精确的解决方案，通过将给定的问题嵌入到一个更大的 家庭（具有更大的自旋，更大的组等）其中小 参数存在，并且通过应用重整化 一种允许人们分阶段处理问题的方法 突然之间 %%% 这项工作将利用为高能物理开发的技术 研究凝聚态系统中的相变， 物质的性质从一种形式转变为另一种形式，例如 当绝缘材料变成一种没有 对电荷流动的阻力。 通常这些阶段 转变作为温度的函数进行研究。 但对于 这项工作的计算将在零温度下进行， 量子效应占主导地位。 要研究的影响是基本的 凝聚态物理和材料中的许多现代问题 科学

Theoretical research will be conducted on quantum phase transitions, that is, phemonena in which the ground state of a many-body system changes qualitatively as some control parameter is varied at zero temperature. These include transitions from metal to insulator as a function of interaction strength, randomness or both, changes in magnetic order with hole density, representation of the spins, or microscopic couplings, and the transition from metal to superconductor with doping. All these problems have the common feature that there is generally no obvious small parameter to allow a clean theoretical calculation. This will be handled in a variety of ways: by working with low dimensional analogs amenable to exact solution, by embedding the given problem in a larger family (with bigger spin, bigger group, etc.) where a small parameter exists, and by the application of the renormalization group which permits one to deal with the problem in stages instead of all at once. %%% This work will utilize techniques developed for high energy physics to investigate phase transitions in condensed matter systems where the properties of matter change from one form to another, such as occurs when an insulating material changes to one which has no resistance to the flow of electric charge. Usually these phase transitions are studied as a function of temperature. However, for this work the calculations will be done at zero temperature where quantum effects dominate. The effects to be studied are basic to many modern problems in condensed matter physics and materials science.