Simulating Majorana fermions in black hole with Ising Models

How can the complex physics of quantum fields in curved spacetime, specifically around a Schwarzschild black hole, be simulated using controllable, tabletop quantum many-body systems? The authors seek to bridge the gap between theoretical predictions of general relativity and experimental accessibility by mapping Majorana fermions to spin chains.

The researchers utilize the transverse-field Ising model as an analog simulator. By applying the Jordan-Wigner transformation, they map the Hamiltonian of a Majorana fermion field in a curved background to a lattice of spins with site-dependent exchange interactions and transverse magnetic fields. They explore multiple coordinate systems—Schwarzschild, tortoise, and Kruskal—to derive corresponding spin Hamiltonians. A key insight is that while these coordinate choices lead to different microscopic spin models, they all flow to the same continuum limit, demonstrating an emergent form of general covariance.

The study establishes that the choice of coordinate system significantly impacts the ease of experimental implementation. Using Schwarzschild coordinates leads to site-dependent exchange couplings, which are difficult to engineer. In contrast, using conformally flat coordinates (such as tortoise or Kruskal) allows for a simplified model where the exchange coupling is constant, and the black hole geometry is encoded entirely in the spatial profile of the transverse magnetic field. The authors demonstrate that this approach can simulate black hole particle production and suggest that spin correlation measurements in these systems can serve as a proxy for detecting Hawking radiation.