Yaron Oz

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.

Photon entanglement is a fundamental resource for quantum technologies, yet it is extremely fragile especially in large quantum circuitry, which is necessary for quantum information processing and computing. We propose an integrated scheme for direct topological protection of entanglement, enabling robust transport of entangled photonic states, even when the photon dynamically evolves during propagation. Our platform relies on a two-dimensional discrete-time quantum walks in synthetic dimensions, supporting topological edge states at the interface between distinct domains. Thus far, in all previous approaches for exploiting topology to protect entanglement, the protection was linked to the position of the photon in the actual structure. In contrast, our scheme relies on a synthetic temporal dimension (time bins) where the entangled state is always reproduced, despite fluctuations or variations that may emerge in the system. Thus, our scheme provides precise temporal control important for synchronization and timing in quantum computation. By suppressing phase-sensitive errors—the most critical noise source in photonic platforms—our approach can lower the physical error rate below fault-tolerance thresholds and reduce the overhead typically required for scalable quantum information processing. The robustness to errors arises from the fact that the entangled state is preserved through correlations in the synthetic (temporal) dimension. As a result, we ensure that at specific designated times, the emergent state faithfully reproduces the initial entangled state, despite the photon having taken any dynamically evolving paths. This approach establishes a robust framework for directly protecting entanglement.

A bstract: We study QED ₂ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as 1/ a ( t ) while the electric term grows as g ² a ( t ), sweeping the spectrum through a moving narrow-gap region in the ( τ , m ) plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later τ as the lattice spacing goes to zero, with current data favoring τ _∗ ≈ 3.1, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED ₂ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.

A bstract: We derive the reduced Dirac Hamiltonian on the non-rotating BTZ background and use its redshift structure to construct a gauge-covariant single-band lattice model on the constant-time BTZ cylinder. In equal-area coordinates the AdS radius L fixes the local Gaussian curvature, while the horizon radius r _h fixes the throat size and the strength of the near-horizon redshift. The lattice model therefore has a direct geometric interpretation and is not presented as an unshown reduction of the two-component Dirac lattice. Its angular Fourier transform yields an exact curved Harper equation with BTZ-dependent hopping amplitudes and a consistent dimensionless angular quasi-momentum. We then supplement global parameter scans with state-resolved diagnostics: spectra color-coded by mean radius, local density of states, direct flux-response versus radius correlations, and Aharonov–Bohm spectral flow and persistent current on the BTZ cycle. These results show that weaker curvature sharpens the butterfly-like fragmentation, whereas larger horizons suppress both magnetic and Aharonov–Bohm response by creating weakly dispersing near-horizon states.

A bstract: We study the real-time chiral dynamics of Dirac fermions in AdS ₂ and AdS ₂ black hole backgrounds. The spacetime curvature generates a spin connection term, acting as an effective magnetic field and a position-dependent chiral chemical potential. This leads to strongly asymmetric wave propagation, confined within an inhomogeneous Lieb-Robinson cone. The front velocities decrease with increasing fermion mass and horizon radius. The entanglement entropy grows inside the causal cone, and it saturates due to screening/dephasing in the finite inhomogeneous chain. In dipole-dipole collision, the central bipartite entropy rises when the inward Lieb-Robinson fronts intersect, forming a bright ridge in the local entanglement profile. Charge and current correlators peak at the front arrival, providing a real-time diagnostic of chiral transport. These results establish a causality-respecting framework, linking curvature and horizons to transport and entanglement in (1+1)-dimensional fermionic matter.