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arXiv · 2410.16582

A Lindbladian for exact renormalization of density operators in QFT

Samuel Goldman·Nima Lashkari·Robert G. Leigh
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Abstract

In arXiv:1609.03493, the authors extended the exact renormalization group (ERG) to arbitrary wave-functionals in quantum field theory (QFT). Applying this formalism, we show that the ERG flow of density matrices is given by a Lindblad master equation. 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 $\lambda \phi^4$ theory, and highlight the role of the dissipative terms in generating the correct flow of couplings. 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.

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Samuel Goldman, Nima Lashkari, Robert G. Leigh. 2024-10-21. A Lindbladian for exact renormalization of density operators in QFT. https://doi.org/10.1103/5vx6-bk2m

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