An investigation of $\mathcal{P}\mathcal{T}$-symmetry breaking in tight-binding chains

Abstract

We consider non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric tight-binding chains where gain/loss optical potentials of equal magnitudes $\pm \mathrm{i}\gamma$ are arbitrarily distributed over all sites. The main focus is on the threshold ${\gamma }_c$ beyond which $\mathcal{P}\mathcal{T}$-symmetry is broken. This threshold generically falls off as a power of the chain length, whose exponent depends on the configuration of optical potentials, ranging between 1 (for balanced periodic chains) and 2 (for unbalanced periodic chains, where each half of the chain experiences a non-zero mean potential). For random sequences of optical potentials with zero average and finite variance, the threshold is itself a random variable, whose mean value decays with exponent 3/2 and whose fluctuations have a universal distribution. The chains yielding the most robust $\mathcal{P}\mathcal{T}$-symmetric phase, i.e., the highest threshold at fixed chain length, are obtained by exact enumeration up to 48 sites. This optimal threshold exhibits an irregular dependence on the chain length, presumably decaying asymptotically with exponent 1, up to logarithmic corrections.

arXiv comment30 pages, 12 figures, 1 table

References in corpus (25)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Non-Hermitian Physics
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Robust and fragile PT-symmetric phases in a tight-binding chain
• Bound states in the continuum in PT-symmetric optical lattices
• Classical Representation of the 1D Anderson Model
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Statistics of finite-time Lyapunov exponents in a random time-dependent potential
• Imaginary Cubic Perturbation: Numerical and Analytic Study
• Origin of maximal symmetry breaking in even PT-symmetric lattices
• Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices
• Exponential number of equilibria and depinning threshold for a directed polymer in a random potential
• Flat bands and PT-symmetry in quasi-one-dimensional lattices
• The Lyapunov exponent of products of random $2\times 2$ matrices close to the identity
• Transport properties in a Non-Hermitian triple-quantum-dot structure
• Fluctuations of random matrix products and 1D Dirac equation with random mass
• Interacting quantum walkers: Two-body bosonic and fermionic bound states
• Real-Time Transport in Open Quantum Systems From $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Impurity models and products of random matrices

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