Berlin 2024 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 1: Many-body Theory I
MP 1.3: Vortrag
Montag, 18. März 2024, 10:20–10:40, HL 001
Wrestling with the finite temperature two dimensional Fermi-Hubbard Model: A Tensor Network Attempt — •Aritra Sinha1,2, Marek M. Rams2, Piotr Czarnik2, and Jacek Dziarmaga2 — 1Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — 2Jagiellonian University, Kraków, Poland
The Fermi Hubbard Model is a simple model of interacting electrons on a lattice. However, solving it in two dimensions has been a long-standing challenge. Recently, progress has been made with tensor network methods like infinite projected entangled pair states (PEPS), especially in understanding its ground states in the infinite-size limit. Despite this, finding finite temperature solutions remains challenging, particularly for larger lattices. Our research uses the Neighborhood Tensor Update (NTU) and infinite PEPS for imaginary time evolution, achieving temperatures as low as 0.17 times the hopping rate. We've observed disruptions in the antiferromagnetic order in lattices with slight doping at strong coupling regimes. To reach even lower temperatures, we developed a new algorithm that applies minimally entangled typical thermal states (METTS) to finite PEPS. In my upcoming presentation, I'll explore the numerical challenges we faced and the innovative tensor network strategies we developed, shedding light on the physics of the under-doped Hubbard model and offering insights applicable to other models. These findings serve as valuable benchmarks for theoretical studies and experiments with ultracold atoms.
Keywords: tensor networks; projected entangled pair states; Fermi-Hubbard model; finite temperature; computational physics