Spin systems as quantum simulators of quantum field theories in curved spacetimes

TL;DR

This paper shows how a one-dimensional spin system can simulate quantum field theories in curved spacetimes, enabling experimental exploration of phenomena like particle production and the Unruh effect.

Contribution

It establishes a novel correspondence between spin models with variable parameters and QFT in curved spacetime, providing a practical platform for simulation and study.

Findings

Simulated particle production in expanding universe using the transverse-field Ising model.

Demonstrated the relation between entanglement Hamiltonian and Rindler Hamiltonian.

Provided a dictionary linking spin system parameters to spacetime metrics.

Abstract

We demonstrate that a quantum field theory (QFT) in general two-dimensional curved spacetimes can be realized by a system of quantum spins or qubits. We consider a spin-1/2 model on a one-dimensional ring with spatially and temporally varying exchange couplings and magnetic fields. This model reduces to a QFT of Majorana fermions in the continuum limit. From this correspondence, we establish a dictionary for translating between the spacetime-dependent parameters of the spin model and the general metric on which the QFT is defined. After addressing the general case, we consider the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric as a simple example. According to the dictionary, the QFT of Majorana fermions on the FLRW metric corresponds to the Ising model with a time-dependent transverse magnetic field. We demonstrate that the production of Majorana particles in the expanding universe can be simulated with the transverse-field Ising model by increasing the strength of the magnetic field. Furthermore, we examine the Unruh effect through the spin system by using our prescription and show the direct relation between the entanglement (or modular) Hamiltonian in the spin system and the Rindler Hamiltonian. This approach provides an experimentally viable system for probing various phenomena in QFT within curved spacetime, while also opening the door to uncovering nontrivial phenomena in spin systems inspired by curved spacetime physics. It offers fresh perspectives on both QFT in curved spacetimes and quantum many-body spin systems, revealing profound connections between these fields.