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.
Highlights
Quantum field theory in curved spacetime is a semiclassical approximation of quantum gravity theory, where the curved background spacetime is treated classically, while the matter fields in the curved spacetime are quantized
Let us exhibit how to use our analog model to study some new features of quantum field theory in curved spacetime: quantum chaos and fastest scrambling of black holes, appearing from the anti–de Sitter (AdS)-conformal field theory (CFT) correspondence
We have shown that a massless scalar or Dirac field in the static (1 + 1)-dimensional curved spacetime can be simulated by some basic models in condensed-matter physics: the bosonic hopping model, the free Hubbard model, and the XY model
Summary
Quantum field theory in curved spacetime is a semiclassical approximation of quantum gravity theory, where the curved background spacetime is treated classically, while the matter fields in the curved spacetime are quantized. A fully successful quantum gravity theory is still not yet available, such a semiclassical approximation framework has offered us a large amount of interesting new phenomena, such as the Hawking radiation of black holes, particle production in an expanding universe, etc. In this paper we show that there exists a one-to-one correspondence between quantum field theories in an arbitrary two-dimensional spacetime and a site-dependent bosonic hopping model, free Hubbard model, or isotropic XY model in quantum many-body systems. As some applications of our analog gravity model, we study Hawking radiation of a black hole and its entanglement, and show that black holes are the most chaotic systems and the fastest scramblers in nature, predictions of the AdS-CFT correspondence. We use a concrete example to show how to use the picture of blackhole physics to learn something about quantum many-body systems
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