SuMaC: Superconductivity and Magnetic Correlations

• Applicant: Dr. Alexander Wietek
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 509755282

The collective behavior of electrons can give rise to a manifold of intriguing emergent phenomena, ranging from high-temperature superconductivity to quantum spin liquids in frustrated magnets. While strong correlations and the quantum mechanical nature of electrons are the essential ingredients of these phenomena, they also render the endeavor of understanding and making quantitative predictions challenging. However, numerical methods for quantum many-body physics have significantly advanced in recent years and demonstrated that solutions to important open problems in the field of strongly correlated electrons have become achievable today. This project aims at addressing the physics of the Hubbard model using modern finite-temperature tensor network methods. Both the Hubbard model as a description of the cuprate superconductors as well as a moiré Hubbard model describing recent twisted moiré materials will be investigated to answer the following questions: Does the Hubbard model exhibit superconductivity? What is the relation between magnetic, superconducting, and stripe orders? How do electron density, geometric frustration, and interaction strength affect the transition temperatures? What is the nature of the pseudogap regime in the underdoped cuprates? What is the effect of a magnetic field and can quantum oscillations detect novel states of matter? Is a linear-in-temperature resistivity, indicative of strange metallicity, realized at low temperatures? As a second frontier, thermal transport in two-dimensional quantum magnets will be studied. Heat transport is sensitive to charge-neutral excitations and can thus probe the dynamics of exotic Mott insulating states. Certain quantum spin liquids manifest themselves by exhibiting quantized thermal Hall conductivity. The aim is to establish fundamental heat transport properties of frustrated quantum magnets. This includes frustrated Heisenberg models on the square and triangular lattice, relevant for both the cuprate and organic superconductors, as well as, the Kitaev-Heisenberg model in a magnetic field as an effective model for the several spin liquid candidate materials. The effects of spin-phonon coupling on thermal transport will be addressed. Both these objectives will be solidly supported by developments of novel matrix-product-state techniques to achieve finite-temperature simulations studying static as well as dynamical observables.

• DFG Programme: Independent Junior Research Groups