Lindbladian for exact renormalization of density operators in QFT

Fliss [.] extended the exact renormalization group (ERG) to arbitrary wave functionals in quantum field theory. Applying this formalism, we show that a Lindblad master equation gives the ERG flow of density matrices. The Lindbladian consists of a “Hamiltonian” term, which is the sum of a scaling and a coarse-graining (disentangling) operator, and a dissipative term with absorption and emission rates for each momentum mode. We consider as examples the flow of Gaussian states and the perturbative ground state of λ ϕ 4 theory and highlight the role of the dissipative terms in generating accurate contributions to the flow of couplings at nontrivial order in λ . Integrating the Lindblad master equation, we find that a finite ERG flow of density matrices is described by a quantum channel. It follows from the data processing inequality that any distinguishability measure of states is an ERG monotone.