Resolving superconductivity and pseudogap physics in oxides: beating the sign problem

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Superconducting (SC) materials, which transport currents without losses, are the basis of advanced medical imaging and energy transmission. They are intensely researched for applications such as circuitry, motors and generators far more efficient than any today. But these applications need strong cooling - at 'best' to about -160 C - as superconductivity requires electron pairs in a collective quantum state, easily disrupted by thermal energy. A central goal of materials theory is thus to systematically design superconductors working at higher temperatures.Yet this has been impossible so far, as for the best superconductors today, based on oxide ceramics, we still do not understand how electron pairs form. Dynamical Mean Field Theory (DMFT) could predict SC properties in the oxides, yielding insight into pair formation, and thus allow designing better superconductors. Yet, DMFT currently cannot do so as it uses Quantum Monte Carlo (QMC) algorithms that suffer from the so-called sign-problem. This project aims to solve key models of SC oxides, especially the high-temperature cuprates, as well as strontium ruthenate. Treating much larger Anderson impurity problems (AIPs) - the basis of DMFT - at much lower temperatures than possible before will allow modelling these oxides in their SC state for the first time, as well as the mysterious pseudogap (PG) and strange metal (SM) states, which precede superconductivity at higher temperature. Understanding these as well is crucial for revealing why electrons pair in the oxides.The project will build on a major advance in so-called parallel density matrix renormalization group (pDMRG) numerics, co-developed by the PI recently. The pDMRG code outperforms QMC for interacting electrons at low temperatures as it does not suffer the sign-problem. The pDMRG is also much more powerful than regular DMRG, distributing a calculation too demanding for single-CPU calculations across many compute nodes of a supercomputer. We will thus re-implement DMFT numerics using pDMRG. The outcome will be a DMFT superior to previous implementations not just quantitatively, but qualitatively. Using it, we will solve AIPs derived from the extended Hubbard model of cuprates as well as multi-orbital AIPs for strontium ruthenate. For strontium ruthenate, we will also be the first to simulate the crossover from the SM state to a near-perfect metallic state around 25 K, which has also been impossible with QMC. For the extended Hubbard model, we will seek to replicate the experimentally found emergence of two separate pseudogaps, one large and one small. This project would yield important insight into the nature of electron-pairing in high-temperature oxide superconductors, by solving the extended 2D Hubbard model for unprecedented system sizes und temperatures. It could be a significant step towards being able to engineer high-temperature superconductors on purpose. This project could further deliver a breakthrough in the understanding of a key model-material for superconductivity, strontium ruthenate. Neither its SM state nor its crossover into a perfect metal is currently understood. This project could thus yield a long-necessary 'sorting' of the competing theories for this model material, with broad impact for the theory of superconductivity, due to this particular material being a clean, near-ideal testing ground for the whole class of phenomena.