Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions

Abstract

We propose a general class of open fermionic models where quadratic Liouvillians governing the dissipative dynamics feature analytically characterized 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 dominant modes of the system at long times, 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 long-time dynamics which can serve as detectable signals for the higher-order Liouvillian EPs.

12 pages, 3 figures

References in corpus (27)

• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian Topology and Exceptional-Point Geometries
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Spectral theory of Liouvillians for dissipative phase transitions
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Phases of Wave Functions and Level Repulsion
• Symmetry-protected multifold exceptional points and their topological characterization
• Spectral theorem for the Lindblad equation for quadratic open fermionic systems
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Liouvillian Skin Effect in an Exactly Solvable Model
• Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$ symmetries
• Generating high-order quantum exceptional points in synthetic dimensions
• $\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics
• Engineering Dissipative Quasicrystals
• Encircling the Liouvillian exceptional points: a brief review
• Chiral Bell-state transfer via dissipative Liouvillian dynamics
• Chiral state transfer under dephasing
• Photonic chiral state transfer near the Liouvillian exceptional point
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps
• Hopf Exceptional Points
• Multi-block exceptional points in open quantum systems