具有周期边界条件的连续矩阵乘积态及其在原子电子学中的应用
Continuous matrix product states with periodic boundary conditions and an application to atomtronics
摘要：
介绍了一种求解一维周期边界条件量子场论的时间演化算法。这是通过将Dirac-Frenkel含时变分原理应用于具有周期边界条件的平移不变连续矩阵乘积态来实现的。此外，该方法还引入了附加的边界自由度来研究量子杂质问题。该算法允许在传输矩阵的频谱中的截止，因此具有有效的计算缩放。特别是，我们研究的原子电子系统的原型的例子-一个相互作用的玻色气体旋转的环形陷阱中存在的局部势垒。
英文摘要：
We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system - an interacting Bose gas rotating in a ring shaped trap in the presence of a localised barrier potential.
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