Matrix-product-state approach for qubit-waveguide systems in real space

We present a matrix-product-state-based numerical approach for simulating systems composed of several qubits and a common one-dimensional waveguide. In the presented approach, the one-dimensional waveguide is modeled in real space. Thus, one can use the advantage of matrix-product states that are suited for simulating low-entangled one-dimensional systems. The price to pay is that the vacuum of the waveguide in this modeling becomes the Bogoliubov vacuum, and one has to consider a not-so-small local Hilbert space for bosonic degrees of freedom. To manage the large local Hilbert space, we adopt the recently proposed single-site schemes. We demonstrate the potential of the presented approach by simulating superradiant phenomena within the Hamiltonian dynamics.