Exactly solvable higher-order Liouvillian exceptional points in dissipative fermionic systems

Abstract: We propose a general class of open fermionic models where quadratic Liouvillians governing the dissipative dynamics feature exactly solvable higher-order exceptional points (EPs). Invoking the formalism of third quantization, we show that, among the multiple EPs of Liouvillian, an EP with its order approaching the system size arises as the quasisteady state of the system, leading to a gapless Liouvillian spectrum. By introducing perturbations, in the form of many-body quantum-jump processes, these higher-order EPs break down, leading to finite Liouvillian gaps with fractional power-law scalings. While the power-law scaling is a signature of the higher-order EP, its explicit form is sensitively dependent on the many-body perturbation. Finally, we discuss the steady-state approaching dynamic which can serve as detectable signals for the higher-order Liouvillian EPs.