We will develop matrix product state (MPS) codes for entangled quantum many-body systems in one spatial dimension including long-range interactions, necessary for the long-range dipole-dipole interaction inherent to ultracold molecules. Our open source codes will be integrated into the ALPS (Algorithms and Libraries for Physics Simulations) package as part of the ALPS collaboration. As more complex molecules approach quantum degeneracy, the number and complexity of many-body models to describe them will also increase substantially. Additionally, searching for emergent phenomena such as quantum order requires exploration of vast parameter spaces and extrapolation using many different system sizes. This requires us to rethink the way in which we design and dispatch simulations and collect and interpret data. Open source tools which are to have a long term impact must be flexible to adapt to different physical degrees of freedom, different Hamiltonians, and different dynamical processes; they must be efficient to manage large parameter exploration; and they must contain powerful tools for extracting data from large simulations. Our proposed MPS algorithms enable us to meet these challenges and be prepared for the next wave of ultracold molecular physics.
Our creation of open source code for matrix product state (MPS) and related methods has the potential for new insights into strongly correlated systems, a standing problem in physics on which we have been able to make only a little progress so far. Strongly correlated systems include high-temperature superconductors, an outstanding problem for energy technology as a sizeable fraction of energy resources are squandered simply in transmission lines; high-temperature materials have the potential to alleviate this loss. MPS methods allow us to explore different models of a quantum computer, including in our main physical subject of ultracold molecules, applied to quantum computing. Finally, the training of students in rigorous numerical techniques and high-performance parallel computing is key to success in a number of arenas in society, from the space program to global climate change to monitoring and managing nation-wide outbreaks of infectious diseases. This award will support such training, and will support a principal investigator involved in that effort from the undergraduate through graduate levels.
