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

Tu, Yi-Ting; Jang, Iksu; Chang, Po-Yao; Tzeng, Yu-Chin

doi:10.22331/q-2023-03-23-960

Cited by 12 publications

(3 citation statements)

References 73 publications

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“…Due to the coalescence of eigenstates, the generic entanglement entropy can diverge. In principle, the critical points have properties that differ from those of the exceptional points in terms of fidelity and fidelity susceptibility [61,62]. However, in the free fermion case studied in Refs.…”

Section: Entanglement Entropy In Critical Systemsmentioning

confidence: 99%

Relating non-Hermitian and Hermitian quantum systems at criticality

Hsieh,

Chang

2023

SciPost Phys. Core

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We demonstrate three types of transformations that establish connections between Hermitian and non-Hermitian quantum systems at criticality, which can be described by conformal field theories (CFTs). For the transformation preserving both the energy and the entanglement spectra, the corresponding central charges obtained from the logarithmic scaling of the entanglement entropy are identical for both Hermitian and non-Hermitian systems. The second transformation, while preserving the energy spectrum, does not perserve the entanglement spectrum. This leads to different entanglement entropy scalings and results in different central charges for the two types of systems. We demonstrate this transformation using the dilation method applied to the free fermion case. Through this method, we show that a non-Hermitian system with central charge c = -4c=−4 can be mapped to a Hermitian system with central charge c = 2c=2. Lastly, we investigate the Galois conjugation in the Fibonacci model with the parameter \phi \to - 1/\phiϕ→−1/ϕ, in which the transformation does not preserve both energy and entanglement spectra. We demonstrate the Fibonacci model and its Galois conjugation relate the tricritical Ising model/3-state Potts model and the Lee-Yang model with negative central charges from the scaling property of the entanglement entropy.

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Section: Entanglement Entropy In Critical Systemsmentioning

confidence: 99%

Relating non-Hermitian and Hermitian quantum systems at criticality

Hsieh,

Chang

2023

SciPost Phys. Core

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“…Fidelity has various definitions in the literature, always relating to the overlap of two quantum states with different parameters. Recently, Tzeng et al [23,24] have used a non-Hermitian fidelity to explore EPs, defined by where δ is a small parameter, 〈L| and |R〉 are the left and right ground states (or any state of interest), and λ could more generally be replaced by any parameter of the Hamiltonian. The fidelity susceptibility χ is the second-order expansion coefficient in δ, which is approximately…”

Section: Motivation From Real λmentioning

confidence: 99%

Exceptional points in the Baxter-Fendley free parafermion model

Henry

Batchelor

2023

SciPost Phys.

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Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a generalisation of this idea to \mathbb{Z}_NℤN-symmetric clock models. In 1989 Baxter discovered a non-Hermitian but \mathcal{PT}𝒫𝒯-symmetric model directly generalising the Ising chain, which was later described by Fendley as a free parafermion spectrum. By extending the model’s magnetic field parameter to the complex plane, it is shown that a series of exceptional points emerges, where the quasienergies defining the free spectrum become degenerate. An analytic expression for the locations of these points is derived, and various numerical investigations are performed. These exceptional points also exist in the Ising chain with a complex transverse field. Although the model is not in general \mathcal{PT}𝒫𝒯-symmetric at these exceptional points, their proximity can have a profound impact on the model on the \mathcal{PT}𝒫𝒯-symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field).

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“…, where n is the number of k points involved in real complex energy changes. For our 2D SSH model, n = 1, Re F 1 2 ( ) = [24]. For non-reciprocal coupling system, this paper discusses its generalized Brillouin region (GBZ), non-Bloch block boundary correspondence and non-Bloch topological invariants [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional Su-Schrieffer-Heeger model with imaginary potentials and nonreciprocal couplings

Wang,

Li,

Zhang

et al. 2024

Phys. Scr.

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We examine the 2D-SSH model and focus on its topological states and skin effects resulting from imaginary potentials and nonreciprocal couplings. Our calculations demonstrate that inducing topological edge and corner states allows for different topological phase transitions in the 2D-SSH model. The topological phase transition is achieved by adjusting the ratio of the intercell electron hopping to the intracell electron hopping. The PT symmetry of the system is destroyed when an imaginary potential is present. If non-reciprocal effects are introduced, then skin effects will be seen. This work contributes to understanding how the interplay between imaginary potentials and nonreciprocal couplings modulates the skin effects and topological states in 2D-SSH model.

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

Cited by 12 publications

References 73 publications

Relating non-Hermitian and Hermitian quantum systems at criticality

Relating non-Hermitian and Hermitian quantum systems at criticality

Exceptional points in the Baxter-Fendley free parafermion model

Two-dimensional Su-Schrieffer-Heeger model with imaginary potentials and nonreciprocal couplings

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