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-Tc1 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. With support through the PIs ERC-Starting Grant, this project combines the advantages of both areas, by advancing the theory of quasi-1D electrons coupled to an electron reservoir. Technically, this build on recent breakthroughs in simulating correlated electrons with parallelized density matrix renormalization group (pDMRG) numerics (with the PIs extensive involvement [1, 2]). Such theory will substantially further the under- standing of open electron systems, and show how to use 1D materials as elements in new superconducting (SC) devices and materials: (1) It will enable a new state of matter, 1D electrons with true SC order. Fluctuations from the elec- tronic reservoir, such as graphene, could drive micron-length nanowires to appear SC at high temperatures. (2) A new approach for deliberately engineering a high-Tc bulk superconductor. In 1D, electron-pairing by repulsive interactions is understood and predictable. 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 reservoir. Developing so called chain-dynamical mean field theory (chain-DMFT) based on pDMRG will allow these materials SC properties to be simulated and understood for the first time. Goal 1 will be pursued by simulating Hubbard ladders, a key model for repulsively paired 1D electrons, in contact with reservoir modes, representing the relevant parts of an coherent electron reservoir, which stabilises superconductivity in the ladder. We will also test the assumptions underlying our technique via Quantum Monte Carlo simulations. Towards Goal 2, infinitely many Hubbard-ladders are coupled to form a bulk material in 3D. Using static mean-field (MF) approximation of the interladder coupling allows self-consistently computing this models ground state using pDMRG on a single ladder. This is the first stage establishing DMRG + MF calculations for these novel high-Tc superconductors, towards the ultimate aim of computing SC Tc and its dependence on microscopic parameters. Goal 3 then will combine techniques from (1) and (2) by solving a correlated multi-site system in contact with self-consistently determined reservoir modes. We will focus on quantitatively resolving, for the first time, the effect that single-electron tunneling has on superconductivity of 2D arrays formed from 1D electrons. [1] Phys. Rev. B, 100(7), 075138 (2019).[2] Comput.Phys.Commun.,185(12):3430–3440,2014. [3] Phys.Rev.X,5(4):041032,2015.[4] Phys.Rev.B,98(20):205128,2018.