Path Integrals Over Matrix Product States: Applications and Extensions

短程量子自旋系统的基态一般可以用矩阵乘积态来表示，这是理论物理学的一个重要发展。为了将矩阵乘积态的理论与量子场论的有力工具结合起来，Chris Hooley和他的一些同事最近发展了一维矩阵乘积态的路径积分，这个项目有三个目的：第一，探索矩阵乘积态路径积分在高维系统中的推广;第二，研究这种路径积分中瞬子过程的性质和物理意义;第三，进一步发展矩阵乘积状态路径积分的应用，以解决阻挫磁物理中的开放问题。

The realisation that the ground states of short-range quantum spin systems can generically be represented by matrix product states is an important recent development in theoretical physics. With the aim of integrating the insights of matrix product states with the powerful tools of quantum field theory, Chris Hooley and some of his colleagues recently developed a path integral over one-dimensional versions of such states.The aim of this project is threefold: first, to explore the extension of this matrix-product-state path integral to higher-dimensional systems; second, to investigate the nature and physical meaning of instanton processes in such path integrals; and third, to develop further applications of the matrix-product-state path integral to open questions in the physics of frustrated magnetism.