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 two-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-ion systems is suggested. As applications of the analog gravity model, we show that they can be used to simulate Hawking radiation of a black hole and to study its entanglement. We also show in the analog model that black holes are the 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 black-hole physics.

• Received 14 June 2019
• Revised 30 September 2019
• Accepted 23 March 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.023107

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society