Bonn 2025 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 5: Collective Effects and Disordered Systems
Q 5.3: Vortrag
Montag, 10. März 2025, 11:30–11:45, HS I PI
Exploiting emergent symmetries in disorder-averaged dynamics — •Mirco Erpelding1, Adrian Braemer2, and Martin Gärttner1 — 1Institute of Condensed Matter Theory and Optics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, 07743 Jena, Germany — 2Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
Symmetries are a key tool in understanding quantum systems and, among many other things, allow efficient numerical simulation of dynamics. Disordered systems usually feature reduced sym- metries and additionally require averaging over many realizations, making their numerical study computationally demanding. However, when studying quantities linear in the time evolved state, i.e. expectation values of observables, one can apply the averaging procedure to the time evolution operator resulting in an effective dynamical map, which restores symmetry on the level of super- operators. In this work, we develop schemes for efficiently constructing symmetric sectors of the disorder-averaged dynamical map using short-time and weak-disorder expansions. To benchmark the method, we apply it to an Ising model with random all-to-all interactions in the presence of a transverse field. After disorder averaging, this system becomes effectively permutation invariant, and thus the size of the symmetric subspace scales polynomially in the number of spins allowing for the simulation of very large systems.
Keywords: Disorder; Spin Systems; Symmetries; Numerical method