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

We present a framework that realizes quantum field theory (QFT) in general two-dimensional curved spacetimes using a quantum spin system. Specifically, we study a spin-1/2 chain on a one-dimensional ring with space- and time-dependent exchange couplings and magnetic fields. In the continuum limit, this model maps to a QFT of Majorana fermions, allowing us to construct a dictionary between the parameters of the spin system and the spacetime metric. As a concrete example, we consider the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and show that a QFT of Majorana fermions on this background corresponds to the transverse-field Ising model with a time-dependent magnetic field. We demonstrate that particle production in an expanding universe can be simulated using this spin model.