Robust and fragile PT-symmetric phases in a tight-binding chain

Abstract

We study the phase-diagram of a parity and time-reversal (PT) symmetric tight-binding chain with $N$ sites and hopping energy $J$, in the presence of two impurities with imaginary potentials $\pm i\gamma$ located at arbitrary (P-symmetric) positions $(m,\bar{m}=N+1-m)$ on the chain where $m\le N/2$. We find that except in the two special cases where impurities are either the farthest or the closest, the PT-symmetric region - defined as the region in which all energy eigenvalues are real - is algebraically fragile. We analytically and numerically obtain the critical impurity potential ${\gamma }_{PT}$ and show that ${\gamma }_{PT}\propto 1/N\to 0$ as $N\to \infty$ except in the two special cases. When the PT symmetry is spontaneously broken, we find that the maximum number of complex eigenvalues is given by $2m$. When the two impurities are the closest, we show that the critical impurity strength ${\gamma }_{PT}$ in the limit $N\to \infty$ approaches $J$ ($J/2$) provided that $N$ is even (odd). For an even $N$ the PT symmetry is maximally broken whereas for an odd $N$, it is sequentially broken. Our results show that the phase-diagram of a PT-symmetric tight-binding chain is extremely rich and that, in the continuum limit, this model may give rise to new PT-symmetric Hamiltonians.

10 pages, 4 figures

References in corpus (6)

• Repulsively bound atom pairs in an optical lattice
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Physics counterpart of the PT non-hermitian tight-binding chain
• Scattering theory with localized non-Hermiticities
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Conditional observability

Cited by in corpus (103)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Experimental Study of Active LRC Circuits with PT-Symmetries
• PT-Symmetric Electronics
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Observation of Defect States in PT-Symmetric Optical Lattices
• Nonlinearly-PT-symmetric systems: spontaneous symmetry breaking and transmission resonances
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Non-Hermitian disorder in two-dimensional optical lattices
• Solitons in a chain of PT-invariant dimers
• Bound states in the continuum in PT-symmetric optical lattices
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Stabilization of solitons in PT models with supersymmetry by periodic management
• Parity-time symmetry in optical microcavity systems
• PT spectroscopy of the Rabi problem
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Degrees and signatures of broken PT-symmetry in (non-uniform) lattices
• Spontaneous PT symmetry breaking in non-Hermitian coupled cavities array
• Gegenbauer-solvable quantum chain model
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• Perfect State Transfer in PT-symmetric Non-Hermitian Networks
• Higher-order exceptional points in all-magnetic structures
• Systems of coupled PT-symmetric oscillators
• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• 2D Solitons in PT-symmetric photonic lattices
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• Origin of maximal symmetry breaking in even PT-symmetric lattices
• Non-Hermitian scattering on a tight-binding lattice
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Flat band in two-dimensional non-Hermitian optical 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
• Hermitian dynamics in a class of pseudo-Hermitian networks
• Flat bands and PT-symmetry in quasi-one-dimensional lattices
• Nonlinear modes in a generalized $\mathcal{P}\mathcal{T}$-symmetric discrete nonlinear Schrödinger equation
• A physical interpretation for the non-Hermitian Hamiltonian
• Quantum catastrophes: a case study
• Hermitian scattering behavior for the non-Hermitian scattering center
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Quantum battery with non-Hermitian charging
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• Non-Hermitian interferometer: Unidirectional amplification without distortion
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain
• Photonic quantum simulations of coupled $PT$-symmetric Hamiltonians
• Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices
• Scattering properties of anti-parity-time symmetric non-Hermitian system
• Exceptional points in oligomer chains
• Decays of degeneracies in PT-symmetric ring-shaped lattices
• $\mathcal{P}\mathcal{T}$ symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model
• Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Quantum transport in non-Hermitian impurity array
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Parity-time symmetry under magnetic flux
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Transport and localization of waves in ladder-shaped lattices with locally $\mathcal{P}\mathcal{T}$-symmetric potentials
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• N-site-lattice analogues of $V(x)=i{x}^3$
• Oscillation death in coupled counter-rotating identical nonlinear oscillators
• Bounded dynamics of finite PT-symmetric magnetoinductive arrays
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Pseudo PT symmetric lattice
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• Robust incoherent perfect absorption
• PT symmetric lattices with a local degree of freedom
• Dynamical evolution of an effective two-level system with PT symmetry
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Emergent localized states at the interface of a twofold $\mathcal{P}\mathcal{T}$-symmetric lattice
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Fractionality and $\mathcal{P}\mathcal{T}$- symmetry in a square lattice
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• Semi-localization transition driven by a single asymmetrical tunneling
• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Fractionality and PT-symmetry in an electrical transmission line
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Instanton calculus without equations of motion: semiclassics from monodromies of a Riemann surface
• Non-orientability induced PT phase transition in Moebius ladder lattices
• An investigation of $\mathcal{P}\mathcal{T}$-symmetry breaking in tight-binding chains
• Edge states and persistent current in a PT-symmetric extended Su-Schrieffer-Heeger model with generic boundary conditions
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• $\mathcal{P}\mathcal{T}$-symmetry in compact phase space for a linear Hamiltonian
• PT-symmetry enabled stable modes in multi-core fiber
• Exceptional spectrum and dynamic magnetization
• Extreme events in the Lienard system with asymmetric potential: An in-depth exploration
• Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation
• Dissipation-induced bound states as a two-level system
• Resilience of $\mathcal{P}\mathcal{T}$ symmetry against stochasticity in a gain-loss balanced oscillator