Spectral gaps of local quantum channels in the weak-dissipation limit
J. Alexander Jacoby, David A. Huse, Sarang Gopalakrishnan
Abstract
We consider the dynamics of generic chaotic quantum many-body systems with no conservation laws, subject to weak bulk dissipation. It was recently observed [T. Mori, Phys. Rev. B 109, 064311 (2024)] that the generator of these dissipative dynamics, a quantum channel $\mathcal{E}$, retains a nonzero gap as the dissipation strength $\ensuremath{\gamma}\ensuremath{\rightarrow}0$ if the thermodynamic limit is taken first. We use a hydrodynamic description of operator spreading in the presence of dissipation to estimate the gap of $\mathcal{E}$ as $\ensuremath{\gamma}\ensuremath{\rightarrow}0$, to calculate the operator-size distribution of the slowest eigenmodes of $\mathcal{E}$, and to relate the gap to the long-time decay rates of autocorrelation functions under unitary Floquet dynamics. We provide a microscopic derivation of this hydrodynamic perspective for random unitary circuits. We argue that the gap in the $\ensuremath{\gamma}\ensuremath{\rightarrow}0$ limit can change nonanalytically as one tunes the parameters of the unitary dynamics.