Parallel DMRG

The density matrix renormalization group (DMRG) is a very powerful approach to simulate 1D interacting quantum systems, in many cases offering quasi-exact precision. It is based on a truncated Hilbert space: the coefficients needed to represent a many-body-wavefunction (or density matrix) in a naive product basis, which would be growing exponentially with system size, are each represented by a series of three-dimensional tensors, with one tensor for each site of the physical lattice.

To extend DMRG to more complex problems of 1D correlated systems coupled to particle reservoirs as well as 2D lattices often requires applying many nodes of a distributed-memory parallel supercomputer to a single calculation. Using the Message Passing Interface (MPI), a standard for distributed computing, pDMRG was designed specifically for this purpose. The code offers three layers of parallelism.

Developing pDMRG was one central goal of the MAQUIS collaboration, running from 2010 to 2013, between the groups of Thierry Giamarchi (University of Geneva), Frederic Mila (EPF Lausanne) and Matthias Troyer (ETH Zürich). The single-node version of pDMRG was already released as part of the redeveloped ALPS-library.

Parallel DMRG for distributed memory supercomputers has seen extensive testing and application to large-scale physics problems of superconductivity in 2D correlated electrons. Further development of this pDMRG is ongoing with, and more information on it can be found from, Theory Group Adrian Kantian.