  We present a novel generalization of the chain mapping technique that applies
to multi-atom, multimode systems by making use of coupling matrix
transformations. This is extremely useful for tensor network simulations of
multimode Dicke model and multi-spin-boson model because their coupling
structures are altered from the star form to the chain form with near-neighbor
interactions. Our approach produces an equivalent Hamiltonian with the latter
coupling form, which we call the band Hamiltonian, and we demonstrate its
equivalence to the multimode Dicke Hamiltonian. In the single atom case, our
approach reduces to the chain mapping technique. When considering several tens
of field modes, we have found that tensor network simulation of two atoms in
the ultrastrong coupling regime is possible with our approach. We demonstrate
this by considering a pair of entangled atoms confined in a cavity, interacting
with thirty electromagnetic modes.
