Efficient tensor network simulation of multi-emitter non-Markovian systems

We present a numerical method to simulate a system of multiple emitters coupled to a non-interacting bath, in any parameter regime. Our method relies on a Block Lanczos transformation that maps the whole system onto a strip geometry, whose width is given by the number of emitters. Utilizing the spatial symmetries of the problem and identifying the relevant range of energies of the bath we achieve a more efficient simulation, which we perform using tensor network techniques. As a demonstration, we study the collective emission from multiple emitters coupled to a square lattice of bosons and observe how the departure from Markovianity as coupling strength and emitter number is increased prevents collective radiation. We also simulate the dynamic preparation of an excitation in a bound state from a multi-excitation initial state. Our work opens new possibilities for the systematic exploration of non-Markovian effects in the dynamics and equilibrium properties of multi-emitter systems. Furthermore, it can easily be extended to other setups, including finite bath temperature or impurities coupled to fermionic environments.