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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.16582 |
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| _version_ | 1866916448728776704 |
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| author | Goldman, Samuel Lashkari, Nima Leigh, Robert G. |
| author_facet | Goldman, Samuel Lashkari, Nima Leigh, Robert G. |
| contents | 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 $λϕ^4$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Lindbladian for exact renormalization of density operators in QFT Goldman, Samuel Lashkari, Nima Leigh, Robert G. High Energy Physics - Theory Statistical Mechanics Quantum Physics 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 $λϕ^4$ 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. |
| title | A Lindbladian for exact renormalization of density operators in QFT |
| topic | High Energy Physics - Theory Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2410.16582 |