Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 3: Quantum-Critical Phenomena (joint session TT/DY)
DY 3.10: Vortrag
Montag, 9. März 2026, 12:00–12:15, HSZ/0101
Spectral Optimization of the 2-Sphere and Applications to Classical and Quantum Interacting Spin Systems — •Jonas Völler1, Grigorios Makris1, Fabian Hassler2, and Stefan Wessel1 — 1Institute for Theoretical Physics, RWTH Aachen University, Germany — 2Institute for Quantum Information, RWTH Aachen University, Germany
We investigate discretizations of the 2-sphere using non-uniform simplicial lattices. Starting from an icosahedral seed, we optimize the lattice by solving the free-particle tight-binding model and applying gradient descent to reduce spectral degeneracy breaking, with the goal of restoring the 2ℓ+1-fold degeneracy of an SO(3)-symmetric system. We then perform Monte Carlo simulations of the critical Ising and Potts models and quantify the rotational symmetry breaking by projecting the two-point correlation function onto spherical harmonics. For sufficiently fine discretizations, we successfully recover the expected SO(3)-symmetric behavior. Finally, we carry out quantum Monte Carlo simulations of the transverse-field Ising model and locate its critical point by studying Binder-cumulant crossings.
Keywords: (Quantum) Criticality; Spin-systems; Spectral Optimization; Spherical Lattices; Monte Carlo