Gradient optimization of finite projected entangled pair states

Understand

The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension.

• However, due to the high computational scaling with the virtual bond dimension $D$, in a practical application PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, the frustrated systems.
• The optimization of the ground state using time evolution method with simple update scheme may go to a larger bond dimension.
• However, the accuracy of the rough approximation to the environment of the local tensors is questionable.