Non-Hermitian Skin Effect Along Hyperbolic Geodesics

Abstract

Recently, it has been revealed that a variety of novel phenomena emerge in hyperbolic spaces, while non-Hermitian physics has significantly enriched the landscape of condensed matter physics. Building on these developments, we construct a geodesic-based method to study the non-Hermitian skin effect (NHSE) in non-reciprocal hyperbolic lattices. Additionally, we develop a geodesic-periodic boundary condition (geodesic-PBC), akin to the Euclidean periodic boundary condition (PBC), that complements its open boundary condition. Importantly, we find that the non-reciprocal directionality within a hyperbolic regular polygon and the geodesic-based boundary determine the spectral sensitivity, and hence, the NHSE. Unlike in Euclidean models, however, we must utilize boundary localization to distinguish non-trivial skin modes from their trivial boundary counterpart due to the extensive boundary volume of hyperbolic lattices. We also relate the spatial density profile with the finite-size scaling of hyperbolic lattices. These aspects highlight the profound impact of hyperbolic geometry on non-Hermitian systems and offer new perspectives on the intricate relationship between the geometric characteristics of hyperbolic lattices and non-Hermitian physics.

13 pages and 10 figures

References in corpus (73)

• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Reciprocal skin effect and its realization in a topolectrical circuit
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• Observation of higher-order non-Hermitian skin effect
• Topological Non-Hermitian skin effect
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Simulating quantum many-body dynamics on a current digital quantum computer
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Second-order topological non-Hermitian skin effects
• Non-Hermitian Linear Response Theory
• Simulating hyperbolic space on a circuit board
• Crystallography of Hyperbolic Lattices
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• Observation of novel topological states in hyperbolic lattices
• Hyperbolic band theory
• Hybrid skin-topological modes without asymmetric couplings
• Topological hyperbolic lattices
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Automorphic Bloch theorems for hyperbolic lattices
• Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
• Non-Hermitian skin clusters from strong interactions
• Hyperbolic band topology with non-trivial second Chern numbers
• Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Dislocation Non-Hermitian Skin Effect
• Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Hyperbolic Topological Band Insulators
• Chern insulator in a hyperbolic lattice
• Universality of Hofstadter butterflies on hyperbolic lattices
• Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices
• Dimensional transmutation from non-Hermiticity
• Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect
• Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
• Non-Hermitian Mott Skin Effect
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Curving the space by non-Hermiticity
• Designing non-Hermitian real spectra through electrostatics
• Zoology of non-Hermitian spectra and their graph topology
• Experimental Detection of the Quantum Phases of a Three-Dimensional Topological Insulator on a Spin Quantum Simulator
• Holographic duality between $(2+1)$-d quantum anomalous Hall state and $(3+1)$-d topological insulators
• Non-Hermitian Squeezed Polarons
• Digital Simulation of Topological Matter on Programmable Quantum Processors
• Unconventional scaling at non-Hermitian critical points
• Geometry-dependent skin effects in reciprocal photonic crystals
• Non-Abelian hyperbolic band theory from supercells
• Quantum phase transitions of interacting bosons on hyperbolic lattices
• Many-Body Non-Hermitian Skin Effect for Multipoles
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Density of states of tight-binding models in the hyperbolic plane
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Hyperbolic non-Abelian semimetal
• Möbius Strip Microlasers: a Testbed for Non-Euclidean Photonics
• Observation of higher-order topological states on a quantum computer
• Experimental observation of exceptional bound states in a classical circuit network
• Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations
• A brief review of hybrid skin-topological effect
• Kinked linear response from non-Hermitian cold-atom pumping
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Spectral and Combinatorial Aspects of Cayley-Crystals
• Growth models on the Bethe lattice
• Non-Hermitian Quantum Fractals
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter

Cited by in corpus (6)

• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Many-body critical non-Hermitian skin effect
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Entanglement phases and phase transitions in monitored free fermion system due to localizations
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Interacting many-body non-Hermitian systems as Markov chains