Quantum Phase Transitions in Condensed Matter

凝聚态物质中的量子相变

• 批准号: 9120525
• 负责人: Ramamurti Shankar
• 金额: $ 17.4万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-12-15 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9120525&HistoricalAwards=false
• 关键词: Quantum; Phase; Transitions; Condensed; Matter

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.

将对量子相变进行理论研究，量子相变是指在零温度下，多体系统的基态随着控制参数的变化而发生质的变化的现象。这些包括从金属到绝缘体的转变，作为相互作用强度的函数，随机性或两者兼有，磁顺序随空穴密度的变化，自旋的表示或微观耦合，以及从金属到掺杂超导体的转变。所有这些问题都有一个共同的特点，即一般没有明显的小参数来进行干净的理论计算。这将通过多种方式处理：通过使用适合精确解的低维类比，通过将给定问题嵌入一个存在小参数的更大的族（具有更大的自旋，更大的群等），以及通过应用重整化群允许人们分阶段处理问题，而不是一次处理所有问题。这项工作将利用为高能物理学开发的技术来研究凝聚态物质系统中的相变，在凝聚态物质系统中，物质的性质从一种形式转变为另一种形式，例如当绝缘材料转变为对电荷流动没有阻力时发生的相变。通常这些相变是作为温度的函数来研究的。然而，对于这项工作，计算将在量子效应占主导地位的零温度下进行。所研究的效应是凝聚态物理和材料科学中许多现代问题的基础。