Quantum Phase Transitions in Condensed Matter

9415796 Shankar重整化群（RG）在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，首席研究员已经构思出一种方法，将其应用于非相对论性电子。 分析产生了很多洞察到各种看似不相交的问题，如朗道费米液体，BCS不稳定性和电荷密度波的形成。 对于那些希望用其他物质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，各种新的问题，量子相变之间的各种状态，如绝缘体，CDW，超导体，反铁磁体;费米子耦合到规范场（如在氧化物）等，将使用该方案解决。 研究人员将追求他的目标，将重整化组（由他针对涉及非相对论电子的一些特定问题定制）应用于凝聚态物理中的各种问题。 重整化群方法是把一个难题分解成小问题，一次解决一个。 因此，它非常适合于在电子或自旋之间发生强相互作用的问题中出现的问题，例如量子反铁磁体和高Tc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.