Quantum Simulation of Fermions in $AdS_2$ Black Hole: Chirality, Entanglement, and Spectral Crossovers

TL;DR

This work builds a lattice model of free Dirac fermions on an $AdS_2$ black hole background to explore how curvature, horizons, and spin-connection induced chirality affect spectra, entanglement, and information scrambling. By discretizing with staggered fermions and mapping to qubits via the Jordan–Wigner transform, the authors derive single-particle dispersions, ground and first-excited states, charge profiles, and half-chain entanglement, and they study dynamics through out-of-time-order correlators and spectral statistics. They demonstrate a chiral gravitational effect manifested as a boundary-induced spin current, reveal a redshift-driven integrable-to-ergodic crossover in level statistics, and show that adding on-site disorder can drive a many-body localization transition, all while analyzing the continuum limit to connect with AdS$_2$ physics. These results provide a controlled, holography-relevant quantum simulator platform for probing curvature, anomalies, and information spreading in curved-space quantum matter with potential relevance to quantum simulation experiments.

Abstract

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 chiral gravitational effect 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 states 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 accelerate scrambling, yet remain within a non-chaotic regime. Finally, we map out an integrable to ergodic crossover via level-spacing statistics and Brody fits, and introduce on-site disorder to drive a many body localization transition.

Figures (31)

• Figure 1: The ground state energy for $N=12$ qubits, with horizon radius $r_{h} =1$ (left) $r_{h} =10$ (right). There is a symmetry: $m\rightarrow -m,~\mu \rightarrow -\mu$. The energy becomes more negative as the horizon radius grows, and as $mL$ and $\mu L$ increase.
• Figure 2: The ground state energy per mass $E_0/m$ as a function of the system size $N$, at $\mu=0, L=1$, for four choices of the horizon radius $r_h\in\{0,\;N/10,\;N/5\}$ (from left to right panels).
• Figure 3: The ground state energy per mass, $\frac{E_0}{m}$, as a function of $N$, at $\mu=0$, for three different fermion masses $mL=2,5,10$ and $L=1$ (from left to right panel), and for three choices of the horizon radius $r_h\in\{0,\;N/10,\;N/5,\;N/2\}$.
• Figure 4: The flat and weighted charges for pure $AdS_2$ ($r_h=0$), two choices of $AdS_2$ radius $L$ (2 vs. 10), and mass $m=0$. The weighted charge is affected by the $AdS$ curvature and differs from the flat charge (left panel). This effect decreases as the radius $L$ increases, $O(\frac{1}{L})$, (right).
• Figure 5: The flat and weighted charges for $AdS_2$ black hole with a large horizon radius ($r_h=100$), two choices of $AdS_2$ radius $L$ (2 vs. 10), and mass $m=0$. The weighted charge is affected by the horizon (site $1$ and its neighborhood). The $AdS$ curvature affects the bulk site, which is large in the left panel since $\frac{L}{r_h}$ is small, and decreases as we increase the radius $L$ (right).