$\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials

Abstract

Parity-time ($\mathcal{P}\mathcal{T}$) symmetric systems are classical, gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies. The eigenvalues of a $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian change from real to complex conjugates at a critical value of gain-loss strength that is called the $\mathcal{P}\mathcal{T}$ breaking threshold. Here, we obtain the $\mathcal{P}\mathcal{T}$-threshold for a one-dimensional, finite Kitaev chain -- a prototype for a p-wave superconductor -- in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, on-site potential, and the distance between the gain and loss sites. In addition to a robust, non-local threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev mo del. In particular, for an even chain with zero on-site potential, we find a re-entrant $\mathcal{P}\mathcal{T}$-symmetric phase bounded by second-order EP contours. Our numerical results are supplemented by analytical calculations for small system sizes.

8 pages, 6 figures

References in corpus (5)

• Visualization of Branch Points in PT-Symmetric Waveguides
• Observation of parity-time symmetry breaking in a single spin system
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Tunable waveguide lattices with non-uniform parity-symmetric tunneling
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box

Cited by in corpus (5)

• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Exceptional points in oligomer chains
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• PT-symmetry enabled stable modes in multi-core fiber
• Floquet topological properties in the Non-Hermitian long-range system with complex hopping amplitudes