Grassmann Matrix Product States as a Tool for Ultracold-atom Model Systems

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This project involves basic research in computational physics at the interface between theoretical ultracold-atom physics and quantum-information theory. These are two very active areas of study, widely regarded as enablers for future quantum-based technologies, including quantum computation. The principal aim of the project is to further the development of variational algorithms for describing non-relativistic continuous model systems. These algorithms can be used to describe model systems of interacting cold-atom gases with mass-imbalance, including in the presence of optical lattices, and/or with mixtures of fermions and bosons. The research will be conducted in close collaboration with students and in an open manner. Broad dissemination is planned by including research-developed computational tools in graduate courses and by disseminating results in multiple venues, including to the general public. The latter will be done in collaboration with Cincinnati's Museum of Natural History and Science and involving students as part of their formative experience in science communication.The new continuum Matrix-Product States (cMPS) ansatz will be the main focus of attention in the proposed research. It constitutes the meeting of ideas coming from the theory of integrable systems and the tensor-network methods of quantum-information theory. Furthermore, cMPS brings in a new alternative to look at one-dimensional quantum field theories (QFTs) from a variational perspective. They provide valuable non-perturbative insights into the structure of strongly-coupled QFTs, whose fundamental nature permeates many different branches of physics. Developing these new theoretical and computational ideas in the context of quantum simulations using cold atoms will bring in an extra dimension of merit and add to the growing synergies between cold-atom experiments and many-body theories. In terms of computational infrastructure, the project will leverage the resources of the Ohio Supercomputing Center.