General properties of fidelity in non-Hermitian quantum systems with PT symmetry

Abstract

The fidelity susceptibility is a tool for studying quantum phase transitions in the Hermitian condensed matter systems. Recently, it has been generalized with the biorthogonal basis for the non-Hermitian quantum systems. From the general perturbation description with the constraint of parity-time (PT) symmetry, we show that the fidelity $\mathcal{F}$ is always real for the PT-unbroken states. For the PT-broken states, the real part of the fidelity susceptibility $\mathrm{Re}[{\mathcal{X}}_F]$ is corresponding to considering both the PT partner states, and the negative infinity is explored by the perturbation theory when the parameter approaches the exceptional point (EP). Moreover, at the second-order EP, we prove that the real part of the fidelity between PT-unbroken and PT-broken states is $\mathrm{Re}\mathcal{F}=\frac{1}{2}$. Based on these general properties, we study the two-legged non-Hermitian Su-Schrieffer-Heeger (SSH) model and the non-Hermitian XXZ spin chain. We find that for both interacting and non-interacting systems, the real part of fidelity susceptibility density goes to negative infinity when the parameter approaches the EP, and verifies it is a second-order EP by $\mathrm{Re}\mathcal{F}=\frac{1}{2}$.

To appear in <Quantum> journal

References in corpus (26)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Topological invariance and global Berry phase in non-Hermitian systems
• Ground state fidelity from tensor network representations
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Ground-state fidelity in one-dimensional gapless model
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Observation of a non-Hermitian phase transition in an optical quantum gas
• Exceptional Point and Cross-Relaxation Effect in a Hybrid Quantum System
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility
• Rényi entropies and negative central charges in non-Hermitian quantum systems
• A non-Hermitian optical atomic mirror
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Fidelity approach to Gaussian transitions
• Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them
• Ground-state fidelity of Luttinger liquids: A wave functional approach
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Quantum phase transition in a non-Hermitian XY spin chain with global complex transverse field
• Fidelity and entanglement entropy for infinite-order phase transitions
• Entanglement entropy and fidelity susceptibility in the one-dimensional spin-1 XXZ chains with alternating single-site anisotropy
• Imaginary-field-driven phase transition for the $2$D Ising antiferromagnet: A fidelity-susceptibility approach

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