Interaction induced dynamical $\mathcal{PT}$ symmetry breaking in dissipative Fermi-Hubbard models

Understand

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 an overall gain term.
• By solving the two-site Lindblad equation with fixed dissipation exactly, we find that the dynamics of 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 multi-site systems and closely related to the $\mathcal{PT}$ symmetry breaking accompanied by appearance of complex eigenvalues of the effective Hamiltonian.