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  • Open Access

Exploiting emergent symmetries in disorder-averaged quantum dynamics

Mirco Erpelding1,*, Adrian Braemer2,†, and Martin Gärttner1,‡

  • *Contact author: mirco.erpelding@uni-jena.de
  • †Contact author: bradrian@gmail.com
  • ‡Contact author: martin.gaerttner@uni-jena.de
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Phys. Rev. B 113, 144206 – Published 28 April, 2026

DOI: https://doi.org/10.1103/9tnk-ljth

Abstract

Symmetries are a key tool in understanding quantum systems, and, among many other things, can be exploited to increase the efficiency of numerical simulations of quantum dynamics. Disordered systems usually feature reduced symmetries 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 at the level of superoperators. 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 large systems.

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Corrections

30 April, 2026

Correction: Errors in Eqs. (1), (2), (6), and (C1) have been fixed. A typographical error in the second sentence of the Acknowledgment section has been fixed.

Article Text

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Outline

Information

Phys. Rev. B 113, 144206– Published 28 April, 2026
  • Received 13 July 2025
  • Revised 27 March 2026
  • Accepted 2 April 2026
  • Corrected 30 April 2026
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