Complex Berry phase and imperfect non-Hermitian phase transitions

Abstract

In many classical and quantum systems described by an effective non-Hermitian Hamiltonian, spectral phase transitions, from an entirely real energy spectrum to a complex spectrum, can be observed as a non-Hermitian parameter in the system is increased above a critical value. A paradigmatic example is provided by systems possessing parity-time (PT) symmetry, where the energy spectrum remains entirely real in the unbroken PT phase while a transition to complex energies is observed in the unbroken PT phase. Such spectral phase transitions are universally sharp. However, when the system is slowly and periodically cycled, the phase transition can become smooth, i.e. imperfect, owing to the complex Berry phase associated to the cyclic adiabatic evolution of the system. This remarkable phenomenon is illustrated by considering the spectral phase transition of the Wannier-Stark ladders in a PT-symmetric class of two-band non-Hermitian lattices subjected to an external dc field, unraveling that a non-vanishing imaginary part of the Zak phase -- the Berry phase picked up by a Bloch eigenstate evolving across the entire Brillouin zone -- is responsible for imperfect spectral phase transitions

arXiv comment14 pages, 5 figures, accepted for publication in the Physical Review B

References in corpus (71)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Berry Phase Effects on Electronic Properties
• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Complex Extension of Quantum Mechanics
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Symmetry and Topology in Non-Hermitian Physics
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Non-Hermitian Topology and Exceptional-Point Geometries
• Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Topological phase transition in non-Hermitian quasicrystals
• Topologically protected midgap states in complex photonic lattices
• Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
• Schrödinger operators with complex potential but real spectrum
• Topological invariance and global Berry phase in non-Hermitian systems
• Optical realization of relativistic non-Hermitian quantum mechanics
• Spectral singularities and Bragg scattering in complex crystals
• Geometric phase around exceptional points
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Topological characterization of chiral models through their long time dynamics
• Non-Bloch band collapse and chiral Zener tunneling
• Measurement of the Zak phase of photonic bands through the interface states of metasurface/photonic crystal
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Bloch-Zener oscillations
• Topological and geometrical aspects of band theory
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Effects of Non-Hermiticity on Su-Schrieffer-Heeger Defect States
• Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
• Quantum Geometric Tensor in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Geometric Phase in PT-Symmetric Quantum Mechanics
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
• Topological multiband photonic superlattices
• Designing non-Hermitian real spectra through electrostatics
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• New supersymmetry-generated complex potentials with real spectra
• Optical Zener-Bloch oscillations in binary waveguide arrays
• Berry phase in atom optics
• A New Class of Adiabatic Cyclic States and Geometric Phases for Non-Hermitian Hamiltonians
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system
• Observation of valley Landau-Zener-Bloch oscillations and pseudospin imbalance in photonic graphene
• Aspects of Berry phase in QFT
• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• A new class of non-Hermitian Hamiltonians with real spectra
• Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry
• Berry-like phases in structured atoms and molecules
• Piecewise Adiabatic Following in Non-Hermitian Cycling
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Complex Berry phase instability in PT-symmetric coupled waveguides
• Probing topological phases in waveguide superlattices
• Non-Hermitian heat engine with all-quantum-adiabatic-process cycle
• Exceptional points in bichromatic Wannier-Stark systems
• Non-Hermitian Bloch-Zener phase transition
• The Berry phase in inflationary cosmology
• Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field

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• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Analogue Hawking radiation as a tunneling in a two-level $\mathcal{P}\mathcal{T}$-symmetric system
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Non-Hermitian magnetic moment
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Survival of Hermitian Criticality in the Non-Hermitian Framework
• Non-orientable Exceptional Points in Twisted Boundary Systems