Dynamical localization transition in the non-Hermitian ℤ2 gauge theory

Abstract Local constraint in lattice gauge theory provides an exotic mechanism inducing disorder-free localization. However, the nonequilibrium dynamics in the non-Hermition lattice gauge model has not been well understood. Here, we investigate the quench dynamics of spinless fermions with nonreciprocal hopping in the ℤ2 gauge field formed from the bond spins. Based on the effective model from duality mapping, the non-Hermitian skin effect, disorder-free localization-delocalization transition, and the real-complex transition of eigenenergies are explored systematically. By identifying the diverse scaling behaviors of quantum mutual information for fermions and spins, we predict that the non-Hermition quantum disentangled liquid presents both in localized and delocalized phase with completely different physical nature, the first comes from the ℤ2 gauge field and the second originates from the non-Hermitian skin effect. We finally show that the nonreciprocal dissipation of fermions leads the quantum information flowing from the fermions to spins. Our results provide new insights to the nonequilibrium dynamics in the gauge field, and can be experimentally verified using ultracold atoms in optical lattices.