Geometry Induced Chiral Transport and Entanglement in $AdS_2$ Background

Abstract

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. Entanglement growth occurs inside the causal cone, and saturates through a string-breaking mechanism driven by screening excitations. In dipole-dipole scattering, 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.

Figures (10)

• Figure 1: Real-time evolution of a single dipole excitation in pure AdS$_2$ showing chiral gravitational wave dynamics. Top panels display the local charge density, and bottom panels the corresponding local entanglement entropy, both simulated using MPS for a chain of $N = 40$ sites with $r_h = 0$. From left to right the fermion mass is $m = 0, 1, 4$. The outward tilted, left-right asymmetric wavefronts illustrate geometry induced chiral propagation arising from the AdS redshift and spin connection term, while entanglement growth remains confined within the inhomogeneous LR cone and slows with increasing $m$.
• Figure 2: Charge and entanglement entropy at horizon radius $r_h = 5$, with other parameters as in Fig. \ref{['fig:dipole_charge_and_EE']}. The presence of the horizon enhances the geometric redshift, producing slower, more asymmetric wavefronts and reduced entanglement growth compared to pure AdS. The smaller $b$ is, the closer it is to the event horizon.
• Figure 3: Time evolution of the bipartite entanglement entropy $\Delta S_{L|R}(t)$ following a single-dipole quench in AdS$_2$ and AdS$_2$ black hole backgrounds ($N = 40$). Left: pure AdS ($r_h = 0$); right: AdS black hole ($r_h = 5$). Curves correspond to fermion masses $m = 0, 1, 4$. The initial linear rise of $\Delta S_{L|R}(t)$ reflects ballistic quasiparticle spreading confined within the LR cone, while the later saturation marks a "string-breaking" regime in which screening excitations suppress further entanglement growth.
• Figure 4: Heatmaps of the charge $|\Delta Q_b(t)|$ (top) and the entanglement entropy $\Delta S_b(t)$ (bottom) with first–passage markers (white dots) and inhomogeneous LR arrival–time bounds from the quench bond $b_0$ (yellow/orange for right/left). All measured fronts lie strictly inside the bound, with a clear chiral left–right asymmetry in the slopes. From left to right: $r_h=0,5$. ($N=40,m=1$) For $r_h \neq 0$, a smaller $b$ means it is closer to the event horizon, where the waves propagates slower.
• Figure 5: Real and imaginary parts of the charge-charge and current-current correlation functions $\Pi_{\mu\nu}(t,x_1,x_0)$ (left panels), and their absolute values (right panels), for the single-dipole quench with $m=1$, $N=40$, and separation $\Delta x = 10$. Results are shown for AdS$_2$ (blue) and AdS$_2$ black hole (orange) backgrounds, with horizon radius $r_h = 5$. Both correlators exhibit a negligible early time signal, followed by a pronounced peak when the right-moving front launched by the dipole reaches the probe site $x_1$, providing a time-of-flight diagnostic of the chiral wave. The current correlator $\Pi_{11}$ shows stronger oscillations and larger amplitude than the charge correlator $\Pi_{00}$, reflecting its enhanced sensitivity to the local couplings that encode the AdS redshift.