Diffusive-to-ballistic crossover of symmetry violation in open many-body systems

Understand

Conservation laws in a quantum many-body system play a direct role in its dynamic behavior.

• Understanding the effect of weakly breaking a conservation law due to coherent and incoherent errors is thus crucial, e.g., in the realization of reliable quantum simulators.
• In this work, we perform exact numerics and time-dependent perturbation theory to study the dynamics of \textit{symmetry violation} in quantum many-body systems with slight coherent (at strength $\lambda$) or incoherent (at strength $\gamma$) breaking of their local and global symmetries.
• We rigorously prove the symmetry violation to be a divergence measure in Hilbert space.