Exploiting emergent symmetries in disorder-averaged quantum dynamics

TL;DR

This paper introduces methods to exploit emergent symmetries in disorder-averaged quantum dynamics, enabling efficient simulation of large disordered quantum systems by restoring symmetry at the superoperator level.

Contribution

The authors develop schemes to construct symmetric sectors of the disorder-averaged dynamical map using short-time and weak-disorder expansions, improving simulation efficiency.

Findings

Disorder averaging can restore symmetry at the superoperator level.

The method enables polynomial scaling of the symmetric subspace with system size.

Applied to an Ising model, the approach allows simulation of large, permutation-invariant systems.

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.