Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution

Many-body approaches to open quantum systems have recently become powerful tools for investigating the detailed role of dissipative environments in diverse non-equilibrium molecular and condensed matter processes. Here, we report the development of an efficient algorithm that utilises a time-dependent variational principle for matrix product states to evolve large system-environment states. By thus capturing all system-environment correlations, we reproduce the highly non-perturbative, quantum-critical dynamics of the zero temperature spin-boson model, and then exploit the many-body information to output a complete time-frequency spectrum of the environmental excitations. We highlight how theoretical 'environmental spectra' could yield valuable insights into a wide range of complex dissipative processes, by showing that correlated motion of modes entangled with the spin can appear with persistent vibrational coherence, in spite of incoherent spin relaxation.