# Simulating quantum field theory in curved spacetime with quantum many-body systems

## TL;DR

This paper introduces a framework linking quantum field theories in curved spacetime to quantum many-body systems, enabling simulations of phenomena like Hawking radiation and black hole chaos using experimental setups such as trapped ions.

## Contribution

It establishes a one-to-one correspondence between quantum fields in curved spacetime and specific quantum many-body models, with potential experimental realizations and applications in simulating black hole physics.

## Key findings

- Massless scalar fields map to site-dependent bosonic hopping models.
- Massless Dirac fields map to Hubbard or XY models.
- Black holes are identified as the fastest scramblers and most chaotic systems.

## Abstract

This paper proposes a new general framework to build a one-to-one correspondence between quantum field theories in static 1+1 dimensional curved spacetime and quantum many-body systems. We show that a massless scalar field in an arbitrary 2-dimensional static spacetime is always equivalent to a site-dependent bosonic hopping model, while a massless Dirac field is equivalent to a site-dependent free Hubbard model or a site-dependent isotropic XY model. A possible experimental realization for such a correspondence in trapped ions system is suggested. As applications of the analogue gravity model, we show that they can be used to simulate Hawking radiation of black hole and to study its entanglement. We also show in the analogue model that black holes are most chaotic systems and the fastest scramblers in nature. We also offer a concrete example about how to get some insights about quantum many-body systems from back hole physics.