Tensor network impurity solvers

Grundner, Martin (2025): Tensor network impurity solvers: simulating quantum materials. Dissertation, LMU München: Fakultät für Physik

Abstract

Transition metal oxides (TMOs) and other quantum materials recently attracted immense interest due to their plethora of functional properties. These properties are often the result of strong electronic correlation effects at low temperatures, rendering their theoretical description challenging. The current state-of-the-art method for the simulation of such materials is dynamical mean field theory (DMFT), which provides an exact description of the kinetic part of the system while approximating the Coulomb interaction as local. In this thesis, we present advances in tensor network based impurity solvers, which we use to simulate intricate TMOs at low temperatures within the DMFT approximation. We discuss both methodological and conceptual developments that result in significant improvements in runtime and accuracy. We introduce a tree tensor network structure, the MT3N, specifically tailored to optimally represent the intricate correlation structure of multi\hyp orbital impurity models. A significant advantage of tensor network based impurity solvers is their ability to compute Green's functions both on the Matsubara axis and directly on the real frequency axis. We developed a new analytic continuation algorithm, MinKL, that allows us to combine those Green's functions to significantly stabilize the procedure and improve its accuracy compared to prevalent algorithms. Additionally, we introduce a novel concept of time evolution by evolving systems along complex time contours. By shifting time evolution away from the real time axis, we significantly curtail entanglement growth, enabling substantial improvements in accuracy and efficiency. We present several complex time contours along with multiple post\hyp processing methods that analytically continue our results back to the real frequency axis. These advancements enable us to resolve the Fermi liquid behavior of a multi-orbital system down to ~0.002 eV. Finally, we use these developments in the study of the transition metal oxide LiV$_2$O$_4$. This material has captivated researchers due to its heavy quasiparticle mass at low temperatures, a rare occurrence outside f\hyp orbital materials. Our algorithmic advancements allow us to propose a new theory describing this compound's emerging heavy fermion regime.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: Tensor Networks, DMFT, Quantum Material, Complex Time
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 530 Physik
• Fakultäten: Fakultät für Physik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 28. März 2025
• 1. Bericht­erstatter:in: Schollwöck, Ulrich