Regensburg 2025 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 17: Correlated Electrons: Method Development
TT 17.9: Vortrag
Dienstag, 18. März 2025, 11:45–12:00, H33
Diagonal isometric tensor product states in two dimensions — •Benjamin Sappler1,2, Masataka Kawano3, and Frank Pollmann1,2 — 1Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany — 3Department of Basic Science, University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
The numerical simulation of quantum many-body systems is a challenging problem due to the exponential growth of Hilbert space with system size. In one spatial dimension this challenge was answered by the Density Matrix Renormalization Group (DMRG) algorithm, which can be understood as a variational method over Matrix Product States (MPS). One of the reasons for the success of DMRG is the existence of a canonical form for MPS that simplifies and speeds up most algorithms. Isometric tensor product states (isoTPS) generalize the canonical form of MPS to tensor networks in two and higher dimensions and have shown first promising results. Here we introduce an alternative canonical form for isoTPS by rotating the lattice by π/4 and introducing auxiliary tensors. We implement the time evolving block decimation (TEBD) algorithm on this new canonical form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices.
Keywords: tensor networks; isometric tensor product states; isoTPS; simulation