“Massively parallel density matrix renormalization group method algorithm for two-dimensional strongly correlated systems and its applications”

The 1st R-CCS International Symposium 18 Feb,2019
""Massively parallel density matrix renormalization group method algorithm for two-dimensional strongly correlated systems and its applications""

A strongly correlated quantum system is a class of quantum systems where many-body interactions play an essential role and cannot be treated by first-principles calculations based on the density functional theory. The density matrix renormalization group (DMRG) procedure is known as one of the most powerful and accurate numerical methods for one-dimensional strongly correlated quantum systems. To the contrary, in the two- or higher-dimensional systems, the DMRG method has been less accurate because to obtain the accurate physical quantities in higher-dimensions the DMRG method requires an exponentially large DMRG truncation number m, which makes the practical calculations impossible by using the standard computer facilities. This difficulty is mentioned by the area-row of the entanglement entropy of a pure state such as the ground state. However, the recent development of supercomputing systems enables us to perform the DMRG calculations even for two-dimensional strongly correlated systems. In the present study, we have developed a massively parallel two-dimensional DMRG algorithm. Using the K computer, we can perform the DMRG calculation by taking a huge m [1-6]. Combing with the kernel polynomial expansion method, we are able to simulate quantum dynamics for two-dimensional strongly correlated quantum systems [7-9]. In this presentation, we show our developed massively parallel DMRG algorithm and its applications.

Shigetoshi Sota
(RIKEN R-CCS)