Building controlled theory for high-temperature superconductors: negative-U Hubbard chains as key testbeds

NAISS 2023/6-227


NAISS Medium Storage

Principal Investigator:

Adrian Kantian


Uppsala universitet

Start Date:


End Date:


Primary Classification:

10304: Condensed Matter Physics



Interacting electrons are at the heart of solid state 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-T_c 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 builds on recent breakthroughs made by the Pi and his group in simulating large 2D and 3D arrays of correlated electrons formed from weakly coupling 1D systems of electrons in parallel, that would be far beyond the grasp of current state-of-the-art methods. This approach combines a matrix product state (MPS)-based description of each 1D system with a static mean field (MF) description of the coupling between the electron system, which we thus term MPS+MF. We have found this MPS+MF approach to be an extremely powerful one, capable of predicting the properties of the 2D/3D array with a surprisingly large degree of accuracy, including the amplitude of the superconducting order parameter, critical temperature for the onset of superconductivity (T_c) and even non-equilibrium many-body dynamics. As a consequence, our new method has the unique ability to describe the properties even of 3D unconventional superconductors, in which electrons pair due to repulsive electron interactions, with quantitatively reliable theory as long as they are build up from weakly coupled 1D electrons. This represents a long-sought goal of condensed-matter theory. The purpose of this SNIC Medium Storage application is therefore to apply our work to quantum simulators (analog quantum computers). Realised in ultracold gases of fermionic atoms confined to optical lattices, these systems are intensely studied for their potential to realise analogue states of high-temperature superconductivity. However, previous theory could not efficiently guide these quantum simulators towards the parameter regimes where such states might be observable within current experimental constraints, and thus these could not yet be detected. With the support of this storage project, we will supply this crucial, as-yet missing information by using our accurate and reliably MPS+MF numerics to identify experimentally feasible parameter regimes in arrays of weakly coupled doped, repulsive-U Hubbard ladders, for which todays quantum simulators could observe states of correlated fermions that would correspond to high-temperature superconductivity.