Capturing Open Quantum System Dynamics with Compact Dressed Hamiltonians

We advance the compact dressed Hamiltonian (CDH) framework to simulate the dynamics of open quantum systems strongly coupled to structured bosonic environments. The CDH approach combines reaction-coordinate mapping with a polaron transformation, incorporating strong system-environment hybridization into a dressed representation before truncating the collective bosonic mode. As a result of this truncation, dynamical features are captured with substantially fewer states than in the original representation. The residual environment is treated using a weak-coupling Markovian quantum master equation. We benchmark the method for spin-boson-type models including a single spin, coupled spins, and spin ensembles, considering both resonant and off-resonant regimes and weak to strong system-bath coupling. Comparisons with hierarchical equations of motion and converged reaction-coordinate calculations demonstrate that the CDH representation systematically approaches the reference dynamics with a compact Hilbert space, accurately reproducing oscillation frequencies, relaxation behavior, and long-time populations over a broad parameter regime. The method further captures cooperative phenomena, including bath-mediated interactions, synchronization between spins, and signatures for collective emission. Beyond efficient time propagation, the CDH framework provides direct access to the spectrum and eigenmodes of the Liouvillian. We demonstrate that slow dynamical modes converge rapidly in the CDH representation, enabling identification of relaxation timescales without fitting time-dependent observables. As a whole, the CDH framework provides an efficient and physical description of strongly coupled open quantum-system dynamics.

Source: arXiv:2610.28358v1 - http://arxiv.org/abs/2610.28358v1 PDF: https://arxiv.org/pdf/2610.28358v1 Original Link: http://arxiv.org/abs/2610.28358v1