Interaction-induced dynamical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetry breaking in dissipative Fermi-Hubbard models

Abstract

We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians with pure loss terms possess parity-time ($\mathcal{PT}$) symmetry if we compensate the system additionally with an overall gain term. By solving exactly the two-site Lindblad equation with fixed dissipation, we find that the dynamics of the rescaled density matrix shows an instability as the interaction increases over a threshold, which can be equivalently described in the scheme of non-Hermitian effective Hamiltonians. This instability is also observed in multisite systems and closely related to the $\mathcal{PT}$-symmetry breaking accompanied by appearance of complex eigenvalues of the effective Hamiltonian. Moreover, we unveil that the dynamical instability of the antiferromagnetic Mott phase comes from the $\mathcal{PT}$-symmetry breaking in highly excited bands, although the low-energy effective model of the non-Hermitian Hubbard model in the strongly interacting regime is always Hermitian. We also provide a quantitative estimation of the time for the observation of dynamical $\mathcal{PT}$-symmetry breaking which could be probed in experiments.