Optimization of the projected entangled pair state algorithm for quantum systems

Abstract

In the numerical calculation, the projected entangled pair state (PEPS) algorithm is the most important tensor network algorithm for two-dimensional strongly correlated electron quantum lattice system. In this paper, the optimization of PEPS for two-dimensional quantum system is discussed. An optimization connection between how to update the PEPS tensor and how to calculate the physical observable is investigated, for the tensor network algorithm based on the PEPS representation, which can greatly improve the utilization of computing resources. In this case, optimized PEPS algorithm, as a powerful tool, can be used to study quantum phase transitions and quantum critical phenomena in the thermodynamic limit of the two-dimensional strongly correlated electron quantum lattice system. Of course, optimization of PEPS algorithm program has many other applications, such as adding U(1) and SO(2) symmetry in PEPS algorithm, etc.