Biorthogonal quantum criticality in non-Hermitian many-body systems

Abstract

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.

arXiv comment7 pages, 4 figures

References in corpus (89)

• Edge states and topological invariants of non-Hermitian systems
• Detecting topological order in a ground state wave function
• 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
• The physics of exceptional points
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Ground state overlap and quantum phase transitions
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Fidelity approach to quantum phase transitions
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Biorthogonal Quantum Mechanics
• Quantum critical scaling of the geometric tensors
• Non-Hermitian Many-Body Localization
• Parity-time-symmetric quantum critical phenomena
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Observation of non-Bloch parity-time symmetry and exceptional points
• Quantum Critical Scaling of Fidelity Susceptibility
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Ground-state fidelity in one-dimensional gapless model
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Non-Hermitian Linear Response Theory
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Quantum fidelity in the thermodynamic limit
• Emergent Fermi surface in a many-body non-Hermitian Fermionic chain
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Many-body approach to non-Hermitian physics in fermionic systems
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Non-Hermitian phase transition from a polariton Bose-Einstein condensate to a photon laser
• Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Many-Body Topological and Skin States without Open Boundaries
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Critical fluctuations at a many-body exceptional point
• Exceptional Spin Liquids from Couplings to the Environment
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Fidelity and criticality of quantum Ising chain with long-range interactions
• The Kibble-Zurek mechanism at exceptional points
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility
• Quantum metric and wavepackets at exceptional points in non-Hermitian systems
• Fidelity susceptibility of the quantum Ising model in the transverse field: The exact solution
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models
• Hybrid exceptional point created from type III Dirac point
• Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model
• Unconventional scaling at non-Hermitian critical points
• Fidelity Susceptibility in the Quantum Rabi Model
• Ground-state fidelity of Luttinger liquids: A wave functional approach
• Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity
• Topological invariants, zero mode edge states and finite size effect for a generalized non-reciprocal Su-Schrieffer-Heeger model
• Fidelity as a probe for a deconfined quantum critical point
• Interaction induced dynamical $\mathcal{P}\mathcal{T}$ symmetry breaking in dissipative Fermi-Hubbard models
• Fidelity susceptibility of the anisotropic $XY$ model: The exact solution
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Numerical studies of ground state fidelity of the Bose-Hubbard model
• Quantum Renormalization Group for Ground-State Fidelity
• Ising chain with topological degeneracy induced by dissipation
• Non-Hermitian Avalanche Effect: Non-Perturbative Effect Induced by Local Non-Hermitian Perturbation on a Z2 Topological Order
• Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition
• Uhlmann fidelities from tensor networks
• Quantum deleting and cloning in a pseudo-unitary system
• Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension
• Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{R}\mathcal{T}$ symmetry
• Topological quasi-one-dimensional state of interacting spinless electrons
• Imaginary-field-driven phase transition for the $2$D Ising antiferromagnet: A fidelity-susceptibility approach

Cited by in corpus (9)

• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Non-Hermitian Squeezed Polarons
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Weak Ergodicity Breaking in Non-Hermitian Many-body Systems
• Symmetry protected exceptional points of interacting fermions
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Dynamical scaling laws in the quantum $q$-state clock chain