Abstract:
Strong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates, giving rise to many-body localized phases. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized one. In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. In this talk, I ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system.
The dissipation is described using non-Hermitian Hamiltonians, which can effectively be obtained from Markovian dynamics conditioned on null measurement. In this non-Hermitian setting, the use of the singular value decomposition is proposed as an effective tool for characterizing dynamical phases. It is thus identified a crossover of the singular values from chaotic to integrable spectral features and of the singular vectors from delocalization to localization. The method is illustrated in an XXZ Hamiltonian with random local dissipation.
