Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks

Abstract

We present a continuous tensor-network construction for the states of quantum fields called cPEPS (continuous projected entangled pair state), which enjoys the same spatial and global symmetries of ground-states of relativistic field theories. We explicitly show how such a state can approximate and eventually converge to the free field theory vacuum and suggest a regularization-independent way of estimating the convergence via a universal term in the fidelity per-site. We also present a detailed bottom-up construction of the cPEPS as the continuum limit of the conventional lattice Projected Entangled Pair State (PEPS).

13 pages, 2 figures

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Cited by in corpus (9)

• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Wilson loops in the Hamiltonian formalism
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Kac-Moody symmetries in one-dimensional bosonic systems
• Variational Neural Network Approach to QFT in the Field Basis
• Holographic Tensor Networks as Tessellations of Geometry