Non-perturbative Approaches to Condensed Matter Physics

[9802813] Fendley非微扰方法对于探索凝聚态物理中大量有趣的强耦合系统是有价值的。实验的进步已经允许对量子霍尔效应、量子杂质和自旋链等系统进行广泛的审查，这些新技术可以立即应用。许多这样的系统表现出完全的非费米液体行为，这意味着人们通常甚至不能制定一个围绕自由电子的微扰理论。本研究计划将利用Bethe ansatz、共形场论、超对称和其他方法在这些强相互作用系统中寻找精确解。在发展精确计算的新方法方面取得了很大进展，并得出了许多数学物理的深刻结果。在霍尔装置上正在进行或计划进行更多的实验，需要做更多的理论工作。可积方法非常强大，但远不能计算一切，即使在那些特殊情况下它们是适用的。仍然有许多有趣的凝聚态物理模型，其中应该适用精确的方法。本研究将开发新的工具，以便用精确的方法处理可积模型。此外，粒子物理学家在理解超对称场论方面取得的惊人进展在凝聚态物理中的应用有限。这个问题也将加以讨论。这项拨款将支持理论研究，以寻找各种系统的精确解决方案，这些系统的特点是电子相互作用如此强烈，以至于传统方法都失败了。要使用的技术是在理论和数学物理中常见的技术，但有时在凝聚态物理问题上的应用有限。* * *

9802813 Fendley Nonperturbative methods are valuable for exploring the large number of interesting systems with strong coupling in condensed matter physics. Experimental advances have allowed extensive scrutiny of systems like the quantum Hall effect, quantum impurities and spin chains where these new techniques are immediately applicable. Many of these systems exhibit fully non-Fermi-liquid behavior, meaning that one usually cannot even formulate a perturbation theory around free electrons. This research program will utilize the Bethe ansatz, conformal field theory, supersymmetry, and other methods of finding exact solutions in these strongly interacting systems. A great deal of progress has been made on developing new methods for exact computations, and a number of deep results of mathematical physics have been derived. More experiments are being done or planned on the Hall devices, and more theoretical work needs to be done. Integrable methods are quite powerful, but are far from computing everything, even in those special cases where they are applicable. There are still many interesting models of condensed matter physics where exact methods should be applicable. This research will develop new tools in order to treat integrable models by exact methods. In addition, the striking progress particle physicists have made in understanding supersymmetric field theories has had only limited application in condensed matter physics. This issue will also be pursued. %%% This grant will support theoretical research on finding exact solutions to a variety of systems characterized by electrons which interact so strongly that conventional methods fail. The techniques to be used are ones which are common throughout theoretical and mathematical physics, but which, sometimes, have had limited application to problems in condensed matter physics. ***