Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks

TL;DR

This paper introduces a continuous tensor-network method, cPEPS, for approximating the ground states of relativistic quantum field theories, demonstrating convergence to free field theory vacua and providing a regularization-independent convergence estimate.

Contribution

It develops the cPEPS framework as a continuum limit of lattice PEPS, enabling accurate approximation of relativistic quantum field states with preserved symmetries.

Findings

cPEPS can approximate free field theory vacua

Convergence to the vacuum state is demonstrated

A universal fidelity term estimates convergence independently of regularization

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).