Matrix Product States and Tensor Product States: A quantum information perspective

ZhengCheng Gu, MIT

Abstract: In the first part, I'll describe quantum phases from a quantum information perspective and explain why Matrix Product States and Tensor Product States are useful to characterize quantum phases. In the second part, I'll describe a generic approach for studying 2D quantum phases with long-range entanglement (such as topological phases). The method is based on (a) a general class of trial wave functions known as Tensor Product States, and (b) a 2D real space renormalization group algorithm for efficiently calculating expectation values for these states. Finally, I'll give several examples and briefly introduce our recent development along this interesting direction.