Quantum Phase Transitions in Condensed Matter

9415796重整化群(RG)在过去的相对论场论和临界现象中已经多次证明了它的价值。在过去的几年里，首席研究员构思了一种将其应用于非相对论电子的方法。这一分析对诸如朗道费米液体、BCS不稳定性和电荷密度波形成等各种看似互不相交的问题有了很好的认识。对于那些希望用其他东西取代朗道的费米液体的人来说，这也是一个很好的诊断。在这项研究中，将利用该方案解决绝缘体、CDW、超导、反铁磁体、费米子耦合到规范场(如氧化物)等不同状态之间的量子相变的各种新问题。这位研究人员将继续实现他的目标，即将RnowMaliztion小组(由他为涉及非相对论电子的一些特定问题量身定做)应用于凝聚态物理中的各种问题。重整化群的方法是把一个困难的问题分解成更小的问题，一次做一个。因此，它非常适合于在电子或自旋之间发生强烈相互作用的问题中出现的问题，例如量子反铁磁体和高T_c材料。

9415796 Shankar The Renormalization Group (RG) has proven its worth many times in the past, in relativistic field theory and critical phenomena. Over the last few years the principal investigator has conceived a way to apply it to nonrelativistic electrons. The analysis has yielded a lot of insight into a variety of seemingly disjoint issues such as Landau Fermi-liquids, BCS instability and Charge Density wave formation. It is also a good diagnostic for those who wish to replace Landau's Fermi-liquid with something else. In this research, a variety of new problems in quantum phase transitions between various states like insulator, CDW, superconductor, antiferromagnet; fermions coupled to gauge fields (as in the oxides) etc., will be addressed using the scheme. %%% The investigator will pursue his goal of applying the Renormaliztion Group (as tailored by him to some specific problems involving nonrelativistic electrons) to a variety of problems in Condensed matter physics. The Renormalization Group approach is to take a difficult problem and break it into smaller ones and do them one at a time. It is ideally suited therefore for questions that arise in problems where strong interactions between electrons or spins occur, such as in Quantum Antiferromagnets and High Tc materials.