Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions

Abstract

The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold close to different topological phase transitions in a non-Hermitian long-range extension of the Kitaev chain. The derivative of the geometric phase, as well as its scaling behavior, shows that systems with different long-range couplings can belong to distinct universality classes. Near certain criticalities, we further find that the Wannier state correlation function associated with extended Berry connection of the ground state exhibits spatially anomalous behaviors. Finally, we analyze the scaling of the quantum geometric tensor near phase transitions across exceptional points, shedding light on the emergence of novel universality classes.

6+4 pages, 4+1 figures, Comments and suggestions are welcome

References in corpus (38)

• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Quantum trajectories and open many-body quantum systems
• Universal non-Hermitian skin effect in two and higher dimensions
• Realization of a minimal Kitaev chain in coupled quantum dots
• Kitaev chains with long-range pairing
• Symmetry and Higher-Order Exceptional Points
• Essay: Where Can Quantum Geometry Lead Us?
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Topological Yu-Shiba-Rusinov chain from spin-orbit coupling
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• Superconducting diode effect due to magnetochiral anisotropy in topological insulator and Rashba nanowires
• Experimental measurement of the divergent quantum metric of an exceptional point
• Liouvillian Skin Effect in an Exactly Solvable Model
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Interplay of topological phases in magnetic adatom-chains on top of a Rashba superconducting surface
• Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states
• Optomechanical realization of the bosonic Kitaev-Majorana chain
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• A non-Hermitian optical atomic mirror
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices
• Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography
• Unconventional scaling at non-Hermitian critical points
• Fidelity susceptibility near topological phase transitions in quantum walks
• Observation of Quantum metric and non-Hermitian Berry curvature in a plasmonic lattice
• Correlating Josephson supercurrents and Shiba states in quantum spins unconventionally coupled to superconductors
• Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems
• Universal scalefree non-Hermitian skin effect near the Bloch point
• Signatures of topological phase transition on a quantum critical line
• Scaling laws for non-Hermitian skin effect with long-range couplings
• Superconducting diodes from magnetization gradients
• Identifying non-Hermitian critical points with quantum metric
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Scaling behavior in a multicritical one-dimensional topological insulator
• Unconventional quantum criticality in a non-Hermitian extended Kitaev chain
• Anisotropy of Yu-Shiba-Rusinov states in NbSe${}_2$