Entanglement Renormalization for Weakly Interacting Fields

Abstract

We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum. A key tool is "quantum circuit perturbation theory," which enables us to systematically construct unitaries that map between wavefunctionals which are Gaussian with arbitrary perturbative corrections. As an application, we construct a local, continuous MERA (cMERA) circuit that maps an unentangled scale-invariant state to the ground state of ${\phi }^4$ theory to 1-loop. Our local cMERA circuit corresponds exactly to 1-loop Wilsonian RG on the spatial momentum modes. In other words, we establish that perturbative Wilsonian RG on spatial momentum modes can be equivalently recast as a local cMERA circuit in ${\phi }^4$ theory, and argue that this correspondence holds more generally. Our analysis also suggests useful numerical ansatzes for cMERA in the non-perturbative regime.

arXiv comment8 pages, 1 figure

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Cited by in corpus (25)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Circuit complexity in interacting QFTs and RG flows
• General Methods for Digital Quantum Simulation of Gauge Theories
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Holographic tensor network models and quantum error correction: A topical review
• Renormalized Circuit Complexity
• Holographic Path-Integral Optimization
• Renormalization Group Flow as Optimal Transport
• Renormalization Group Circuits for Weakly Interacting Continuum Field Theories
• Non-Gaussian Entanglement Renormalization for Quantum Fields
• Entanglement Renormalization for Interacting Field Theories
• Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions
• Entanglement renormalization for gauge invariant quantum fields
• Bosonic entanglement renormalization circuits from wavelet theory
• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• The Large $N$ Limit of icMERA and Holography
• Exact Renormalization of Wave Functionals yields Continuous MERA
• Adiabatic ground state preparation in an expanding lattice
• Entanglement Renormalization of a $T\bar{T}$-deformed CFT
• Entanglement Renormalization of the class of Continuous Matrix Product States
• On the Entanglement Entropy in Gaussian cMERA
• A Lindbladian for exact renormalization of density operators in QFT
• Entanglement renormalization for quantum fields with boundaries and defects
• Ground States of the ${\varphi }^4$ Double-Well QFT
• Holography of Transmission Lines: Insights of Continuous MERA and AdS/CFT