PT-symmetry breaking and universal chirality in a PT-symmetric ring

Abstract

We investigate the properties of an $N$-site tight-binding lattice with periodic boundary condition (PBC) in the presence of a pair of gain and loss impurities $\pm i\gamma$, and two tunneling amplitudes $t_0,t_b$ that are constant along the two paths that connect them. We show that the parity and time-reversal ($\mP\mT$)-symmetric phase of the lattice with PBC is robust, insensitive to the distance between the impurities, and that the critical impurity strength for PT-symmetry breaking is given by ${\gamma }_{PT}=|t_0-t_b|$. We study the time-evolution of a typical wave packet, initially localized on a single site, across the PT-symmetric phase boundary. We find that it acquires chirality with increasing $\gamma$, and the chirality reaches a universal maximum value at the threshold, $\gamma ={\gamma }_{PT}$, irrespective of the initial location of the wave packet or the lattice parameters. Our results imply that PT-symmetry breaking on a lattice with PBC has consequences that have no counterpart in open chains.

arXiv comment5 pages, 3 figures

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• Discrete vortex solitons and PT symmetry
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• Tight-binding lattices with an oscillating imaginary gauge field
• Towards nanoscale multiplexing with parity-time symmetric plasmonic coaxial waveguides
• Long-range entangled zero-mode state in a non-Hermitian lattice
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• Parity-time symmetry under magnetic flux
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• PT symmetric lattices with a local degree of freedom
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• Spectra, eigenstates and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric ring
• Semi-localization transition driven by a single asymmetrical tunneling
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• Exceptional spectrum and dynamic magnetization