Quantum simulation of fermions in AdS2 black hole: chirality, entanglement, and spectral crossovers

A bstract We consider free Dirac fermions on a discretized AdS 2 black hole background, and analyze how curved-space redshift, horizons, and the spin-connection-induced fixed-background chiral geometric response shape spectral, transport, and scrambling phenomena. The system is discretized via staggered fermions followed by the Jordan-Wigner transform to encode the model in qubit degrees of freedom, whose Hamiltonian carries site-dependent warp factors and bond-chirality terms encoding the redshift and spin connection effects. We calculate the ground-state and first-excited-state energies, their local charge profiles, and their half-chain entanglement entropies, showing how redshift and chirality affect the transition from criticality to a gapped regime. Probing operator growth via out-of-time-order correlators, we find that horizons and the chiral coupling modify finite-size operator-growth envelopes, while the quadratic model remains non-chaotic. Finally, we characterize a finite-size crossover in level-spacing statistics using adjacent-gap ratios and Brody fits, and introduce on-site disorder to study a disorder-induced localization crossover diagnosed by imbalance plateaux.