Building controlled theory for high-temperature superconductors: negative-U Hubbard chains as key testbeds
Title: Building controlled theory for high-temperature superconductors: negative-U Hubbard chains as key testbeds
SNIC Project: SNIC 2021/6-240
Project Type: SNIC Medium Storage
Principal Investigator: Adrian Kantian <>
Affiliation: Uppsala universitet
Duration: 2021-08-04 – 2022-07-01
Classification: 10304


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 allow us to characterise the power of the MPS+MF approach for superconducting systems in detail. We thus plan to make a systematic study of 3D arrays formed from 1D chains, each chain realising a 1D negative-U Hubbard model, by running extensive calculations on the Tetralith cluster. This will entail running our algorithm for many different chain lengths L, bond dimension chi (this parameter controls the accuracy of the approximation inherent in the MPS approach), electron interactions U, inter-chain coupling t_perp, electron density, and temperature T. The MF-component within our approach means that it is not enough to find the steady state at a given T for all these parameters once, but many times over, until self-consistency is achieved.