The standard block RG and DMRG for open systems

For physical models that can be described by a lattice, a coarse-graining transformation is defined according to the numerical Wilson renormgroup. We formulated a numerical RG method for open quantum systems. To create it, on the one hand, we used the information about how the Hamiltonian is transformed in the standard method defined for Hamiltonian systems and, on the other hand, the knowledge how the Hamiltonian enters the right part of the GKLS equation. After that we have shown exactly how the environment given by Lindblad operators can be inscribed into a well known alternative to the standard method – the DMRG. In the prospects using the methods of numerical renormgroup for open systems allow us to investigate the time behaviour of quantum entanglement. Using the DMRG example for the Ising model in the transverse field, we have demonstrated the behaviour of entanglement for a small iteration number. •The Lindblad equation (also known as Franke-Gorini-Kossakowski-Lindblad-Sudarshan equation) can be viewed in terms of a numerical RG.•RG - transformation of the Lindblad operators is the same as one of the Hamiltonian of the system under consideration.•Using the methods of numerical renormgroup for open systems allow us to investigate the time behaviour of quantum entanglement.