Simulating quantum field theory in curved spacetime with quantum many-body 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.