Probing non-Hermitian phase transitions in curved space via quench dynamics

Abstract

Non-Hermitian Hamiltonians are relevant to describe the features of a broad class of physical phenomena, ranging from photonics and atomic and molecular systems to nuclear physics and mesoscopic electronic systems. An important question relies on the understanding of the influence of curved background on the static and dynamical properties of non-Hermitian systems. In this work, we study the interplay of geometry and non-Hermitian dynamics by unveiling the existence of curvature-dependent non-Hermitian phase transitions. We investigate a prototypical model of Dirac fermions on a sphere with an imaginary mass term. This exactly-solvable model admits an infinite set of curvature-dependent pseudo-Landau levels. We characterize these phases by computing an order parameter given by the pseudo-magnetization and, independently, the non-Hermitian fidelity susceptibility. Finally, we probe the non-Hermitian phase transitions by computing the (generalized) Loschmidt echo and the dynamical fidelity after a quantum quench of the imaginary mass and find singularities in correspondence of exceptional radii of the sphere.

5+5 pages, 6 figures

References in corpus (26)

• Topological Origin of Non-Hermitian Skin Effects
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Dynamics of Loschmidt echoes and fidelity decay
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Electromagnetic wormholes and virtual magnetic monopoles
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Chiral anomaly from strain-induced gauge fields in Dirac and Weyl semimetals
• Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels
• Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
• Magnetic moments in the presence of topological defects in graphene
• Loschmidt Echo Revivals: Critical and Noncritical
• Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices
• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Spherical topological insulator
• Pseudo-magnetic field in curved graphene
• Landau Level Quantization on the Sphere
• Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations
• Hermiticity of the Dirac Hamiltonian in Curved Spacetime
• Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase
• Strain-induced Landau Levels in arbitrary dimensions with an exact spectrum
• Graphene with geometrically induced vorticity
• Interacting surface states of three-dimensional topological insulators
• Spheroidal geometry approach to fullerene molecules
• Test of the Atiyah-Singer Index Theorem for Fullerene with a Superconducting Microwave Resonator
• The construction of a general inner product in non-Hermitian quantum theory and some explanation for the nonuniqueness of the C operator in PT quantum mechanics

Cited by in corpus (2)

• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric