Dynamical chirality production in one dimension

We discuss the quantum computation of dynamical chirality production in lattice gauge theory. Although the chirality of a lattice fermion is complicated in general dimensions, it can be simply formulated on a one-dimensional lattice. The chiral fermion formalism enables us to extract the physical part of the chirality production that would be interpreted as the chiral anomaly in the continuous theory. We demonstrate the computation of the $Z_2$ lattice gauge theory on a classical emulator.

Figure 1

Time evolution of the free Wilson fermion. The fermion number $⟨Q⟩$, the conserved chiral charge $⟨Q^5⟩$, the naive chiral charge $⟨Q_{\text{naive}}^5⟩$, and the energy $⟨H⟩$ are shown. The simulation was done by a noiseless emulator and the error bar is a statistical error.

Figure 2

Time evolution of the Wilson fermion with the $Z_2$ gauge field. The fermion number $⟨Q⟩$, the conserved chiral charge $⟨Q^5⟩$, the naive chiral charge $⟨Q_{\text{naive}}^5⟩$, and the energy $⟨H⟩$ are shown. The simulation was done by a noiseless emulator and the error bar is a statistical error. The gauge parameter is fixed at $\lambda =1$.