Emergent gauge theory and gravity in condensed matter systems

由于存在大量的耦合自由度，从第一性原理计算来理解相关多体系统是很困难的。然而，尽管系统在微观长度尺度上很复杂，但长距离特性可以用一个相对简单有效的理论来描述。有效理论可以作为多体态的表征，因为不同的相可以用不同的有效理论来描述。到目前为止，在凝聚态体系中已经实现了几种不同的相。它们包括朗道费米液态、对称破缺态和分数量子霍尔系统的拓扑有序相。另一方面，我们知道宇宙的真空是由更丰富有效的理论描述的，包括规范理论、广义相对论和（可能的）超对称。因此，人们可以问，这些有效的理论是否也可能出现在某些凝聚态体系中。本研究的目的是寻找具有规范理论、广义相对论或超对称特征的凝聚态系统的新状态。

It is difficult to understand correlated many-body systems from a first principle calculation due to the huge number of coupled degrees of freedom. However, despite the complexity of the system at the microscopic length scale, the long distance properties can be described by a relatively simple effective theory. Effective theory can serve as a characterization of the many-body state in the sense that different phases are described by different effective theories. Until now, several different phases have been realized in condensed matter systems. They include the Landau Fermi liquid state, the symmetry broken state and the topologically ordered phase of the fractional quantum Hall systems. On the other hand we know that the vacuum of our universe is described by richer effective theories which include gauge theory, general relativity and (possibly) supersymmetry. Therefore one can ask whether these effective theories may also emerge in some condensed matter systems. The objective of this research is to search for new states of condensed matter systems whose long distance properties are characterized by gauge theory, general relativity or supersymmetry.