Quantum simulating continuum field theories with large-spin lattice models

TL;DR

This paper presents a method to simulate continuum scalar quantum field theories using large-spin lattice models, enabling quantitative predictions and the study of non-equilibrium phenomena with quantum simulators.

Contribution

It introduces a regularization scheme for scalar QFTs with multi-level systems, demonstrating continuum limit extrapolations and applications to soliton dynamics and non-integrable models.

Findings

Quantitative agreement with sine-Gordon QFT observables.

Successful preparation and scattering of soliton excitations.

Observation of string breaking and plasma oscillations in perturbed models.

Abstract

Simulating the real-time dynamics of quantum field theories (QFTs) is one of the most promising applications of quantum simulators. Regularizing a bosonic QFT for quantum simulation purposes typically involves a truncation in Hilbert space in addition to a discretization of space. Here, we discuss how to perform such a regularization of scalar QFTs by explicitly constructing suitable many-body lattice Hamiltonians using multi-level or qudit systems, and show that this enables quantitative predictions in the continuum limit by extrapolating results obtained for large-spin models. With extensive matrix-product state simulations, we numerically demonstrate the sequence of extrapolations that leads to quantitative agreement of observables for the integrable sine-Gordon (sG) QFT. We further show how to prepare static and moving soliton excitations, and analyze their scattering dynamics in the continuum limit, in agreement with a semi-classical model and with quantitative analytical predictions. Finally, we illustrate how a non-integrable perturbation of the sG model gives rise to dynamics reminiscent of string breaking and plasma oscillations in gauge theories. Our methods are directly applicable in state-of-the-art analog quantum simulators, opening the door to quantitatively investigating a wide variety of scalar field theories and tackling long-standing questions in non-equilibrium QFT like the fate of the false vacuum.