Phys. Rev. Research 2, 023107 (2020)
Simulating quantum field theory in curved spacetime with quantum many-body systems
Run-Qiu Yang1, Hui Liu2, Shining Zhu2, Le Luo3 and Rong-Gen Cai4,*
1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Yaguan Road 135, Jinnan District, 300350 Tianjin, People's Republic of China
2 National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, Jiangsu 210093, People's Republic of China
3 School of Physics and Astronomy, Sun Yat-sen University, 519082 Zhuhai, People's Republic of China
4 CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
* cairg@itp.ac.cn
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 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.
