Real-time chiral dynamics from a digital quantum simulation

The chiral magnetic effect in a strong magnetic field can be described using the chiral anomaly in the $(1+1)$-dimensional massive Schwinger model with a time-dependent $\theta$ term. We perform a digital quantum simulation of the model at finite $\theta$ angle and vanishing gauge coupling using an IBM-Q digital quantum simulator, and observe the corresponding vector current induced in a system of relativistic fermions by a global chiral quench—a sudden change in the chiral chemical potential or $\theta$ angle. At finite fermion mass, there appears an additional contribution to this current that stems from the nonanomalous relaxation of chirality. Our results are relevant for the real-time dynamics of chiral magnetic effect in heavy ion collisions and in chiral materials, as well as for modeling high-energy processes at hadron colliders.

Figure 1

$t/S$ dependence of the vector current following the ${\mu }_5$ quench, with lattice size $N=12$, fermion mass $M=0.1w$, and chiral chemical potential ${\mu }_5=0.2w$. The error bar for each data point represents the statistical error which is estimated by performing 100 000 measurements. The solid lines are exact results. The discretization error becomes significant for $wt/S=1.0$.

Figure 2

Vector current densities after the ${\mu }_5$ quench with lattice size $N=12$ and temporal lattice spacing $wt/S=0.3$. The fermion mass is set to be (a) $M=0.1w$ and (b) $M=0.5w$. The error bar for each data point represents the statistical errors which are estimated by performing 100 000 measurements. The solid lines are exact results.

Figure 3

Vector currents after the $\theta$ quench with lattice size $N=12$ and temporal lattice spacing $wt/S=0.3$. The fermion mass is set to be (a) $M=0.1w$ and (b) $M=0.5w$. The error bar for each data point represents the statistical errors which are estimated by performing 100 000 measurements. The solid lines are exact results.

Figure 4

Short-time behavior of the vector current following the $\theta$ quench with lattice size $N=12$ and fermion mass $M=0.1w$. The data points are obtained by exact diagonalization and dashed lines are short-time behavior of the current (B6).