Hamiltonian truncation tensor networks for quantum field theories

TL;DR

This paper introduces a tensor network method combining Hamiltonian truncation for classical simulation of quantum field theories, enabling precise study of low-energy states and dynamics in models like sine-Gordon and Schwinger.

Contribution

The work develops an exact matrix product state representation of global projectors within a Hamiltonian truncation tensor network framework, improving accuracy over traditional methods.

Findings

Accurately reproduces ground state properties of sine-Gordon model.

Locates the critical point of the Schwinger model.

Studies entanglement growth in quantum quenches.

Abstract

Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly challenging. In this work, we introduce a tensor network method for the classical simulation of continuous quantum field theories that is suitable for the study of low-energy eigenstates and out-of-equilibrium time evolution. The method is built on Hamiltonian truncation and tensor network techniques, bridging the gap between two successful approaches. One of the key developments is the exact construction of matrix product state representations of global projectors, crucial for the implementation of interacting theories. Despite featuring a relatively high computational effort, our method dramatically improves predictive precision compared to exact diagonalisation-based Hamiltonian truncation, allowing the study of so far unexplored parameter regimes and dynamical effects. We corroborate trust in the accuracy of the method by comparing it with exact theoretical results for ground state properties of the sine-Gordon model. We then proceed with discussing $(1+1)$-dimensional quantum electrodynamics, the massive Schwinger model, for which we accurately locate its critical point and study the growth and saturation of momentum-space entanglement in sudden quenches.