Correlated electrons are at the forefront of condensed matter theory. Interacting quasi-1D electrons have seen vast progress in analytical and numerical theory, and thus in fundamental understanding and quantitative prediction. Yet, in the 1D limit fluctuations preclude important technological use, particularly of superconductors. In contrast, high-Tc superconductors in 2D/3D are not precluded by fluctuations, but lack a fundamental theory, making prediction and engineering of their properties, a major goal in physics, very difficult. This project aims to combine the advantages of both areas by making major progress in the theory of quasi-1D electrons coupled to an electron bath, in part building on recent breakthroughs (with the PIs extensive involvement) in simulating 1D and 2D electrons with parallelized density matrix renormalization group (pDMRG) numerics. Such theory will fundamentally advance the study of open electron systems, and show how to use 1D materials as elements of new superconducting (SC) devices and materials: 1) It will enable a new state of matter, 1D electrons with true SC order. Fluctuations from the electronic liquid, such as graphene, could also enable nanoscale wires to appear SC at high temperatures. 2) A new approach for the deliberate engineering of a high-Tc superconductor. In 1D, how electrons pair by repulsive interactions is understood and can be predicted. Stabilization by reservoir - formed by a parallel array of many such 1D systems - offers a superconductor for which all factors setting Tc are known and can be optimized. 3) Many existing superconductors with repulsive electron pairing, all presently not understood, can be cast as 1D electrons coupled to a bath. Developing chain-DMFT theory based on pDMRG will allow these materials SC properties to be simulated and understood for the first time. 4) The insights gained will be translated to 2D superconductors to study how they could be enhanced by contact with electronic liquids.
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