Non-perturbative Approaches to Condensed Matter Physics

9802813芬德利非微扰方法对于探索凝聚态物理中大量具有强耦合的有趣系统是很有价值的。实验的进步使人们能够对量子霍尔效应、量子杂质和自旋链等系统进行广泛的审查，这些新技术立即适用于这些系统。这些系统中的许多都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围绕自由电子建立微扰理论。这项研究计划将利用Bethe ansatz、保形场理论、超对称性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已经取得了很大的进展，并得出了一些数学物理的深刻结果。更多的实验正在或计划在霍尔器件上进行，还需要做更多的理论工作。可积方法非常强大，但远远不能计算一切，即使在那些适用的特殊情况下也是如此。仍然有许多有趣的凝聚态物理模型，在这些模型中应该使用精确的方法。这项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理论方面取得的惊人进步，在凝聚态物理中的应用有限。这一问题也将得到解决。这笔赠款将支持为各种以电子为特征的系统寻找精确解的理论研究，这些系统的相互作用如此强烈，以至于传统方法无法实现。要使用的技术在整个理论和数学物理中是常见的，但有时在凝聚态物理中的应用有限。***

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. ***