Unconventional scaling at non-Hermitian critical points

Abstract

Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or temporal divergences render the thermodynamic limit ill-defined. In this work, we show that a thermodynamic grand potential can still be defined in pseudo-Hermitian Hamiltonians, and can be used to characterize aspects of criticality unique to non-Hermitian systems. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) model as a paradigmatic example, we demonstrate the fractional order of topological phase transitions in the complex energy plane. These fractional orders add up to the integer order expected of a Hermitian phase transition when the model is doubled and Hermitianized. More spectacularly, gap preserving highly degenerate critical points known as non-Bloch band collapses possess fractional order that are not constrained by conventional scaling relations, testimony to the emergent extra length scale from the skin mode accumulation. Our work showcases that a thermodynamic approach can prove fruitful in revealing unconventional properties of non-Hermitian critical points.

arXiv comment19 pages (14 pages of text+ 5 pages of appendices and references), 13 figures. Minor modifications added in the second version

References in corpus (69)

• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Entanglement in quantum critical phenomena
• Edge states and topological invariants of non-Hermitian systems
• Quantized Electric Multipole Insulators
• Aspects of Holographic Entanglement Entropy
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Bloch Band Theory of Non-Hermitian Systems
• Topological energy transfer in an optomechanical system with exceptional points
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Quantum phase transitions
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Critical non-Hermitian Skin Effect
• Universality of Entropy Scaling in 1D Gap-less Models
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Critical Percolation in Finite Geometries
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• New topological invariants in non-Hermitian systems
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Entanglement Entropy and the Fermi Surface
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Non-Bloch band collapse and chiral Zener tunneling
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Unraveling non-Hermitian pumping: emergent spectral singularities and anomalous responses
• Exceptional rings protected by emergent symmetry for mechanical systems
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Helical damping and anomalous critical non-Hermitian skin effect
• Band structure engineering of ideal fractional Chern insulators
• Non-hermitian quantum thermodynamics
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• The Big World of Nanothermodynamics
• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
• Universality classes of topological phase transitions with higher-order band crossing
• Ultrafast and Anharmonic Rabi Oscillations between Non-Bloch-Bands
• Thermodynamics of nonadditive systems
• Multi-critical Behavior in Topological Phase Transitions
• Universalities of thermodynamic signatures in topological phases
• Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations
• Weakly Interacting Topological Insulators: Quantum Criticality and Renormalization Group Approach
• Non-Hermitian topology of one-dimensional spin-torque oscillator arrays
• Generating quantum multi-criticality in topological insulators by periodic driving
• Scaling Theory of ${\mathbb{Z}}_2$ Topological Invariants
• Hill's nano-thermodynamics is equivalent with Gibbs' thermodynamics for curved surfaces
• Thermodynamic signatures of edge states in topological insulators
• Unifying topological phase transitions in noninteracting, interacting, and periodically driven systems
• Domain walls and Schramm-Loewner evolution in the random-field Ising model
• Area Law for Gapless States from Local Entanglement Thermodynamics
• Staircase to Higher-Order Topological Phase Transitions
• Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems
• Internal Geometric Friction in a Kitaev Chain Heat Engine
• Thermodynamics of a Higher-Order Topological Insulator
• Decoding quantum criticalities from fermionic/parafermionic topological states

Cited by in corpus (28)

• Topological Non-Hermitian skin effect
• Impurity induced scale-free localization
• Exceptional Bound States and negative Entanglement Entropy
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Entanglement Hamiltonian in the non-Hermitian SSH model
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Field Theoretical Study of Disorder in Non-Hermitian Topological Models
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• Nonlinear Hall effects with an exceptional ring
• Many-body critical non-Hermitian skin effect
• Universal scaling in far-from-equilibrium quantum systems: an equivalent differential approach
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Deterministic scale-invariant dynamics in a logistic Game-of-Life model
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Interacting many-body non-Hermitian systems as Markov chains
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
• Electronic states in a bilayer graphene quantum ripple
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model
• Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems