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

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

doi:10.48550/arxiv.2203.01834

Cited by 3 publications

(3 citation statements)

References 63 publications

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“…We take ε=10 −3 . The fidelity susceptibility is found to be able to detect both the quantum critical point (χ F =+∞) and the EP (χ F =−∞) [38,39]. As shown in Fig.…”

Section: −F (γ)mentioning

confidence: 87%

Rényi entropies and negative central charges in non-Hermitian quantum systems

Tzeng

Chang

2022

SciPost Phys.

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Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and Rényi entropies to non-Hermitian quantum systems. There have been other proposals for the computation of these quantities, which are distinct from what is proposed in the current paper. We demonstrate the proposed entanglement quantities which are referred to as generic entanglement and Rényi entropies. These quantities capture the desired entanglement properties in non-Hermitian critical systems, where the low-energy properties are governed by the non-unitary conformal field theories (CFTs). We find excellent agreement between the numerical extrapolation of the negative central charges from the generic entanglement/Rényi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/Rényi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic n-th Rényi entropy captures the expected entanglement property, whereas the traditional Rényi entropy can exhibit unnatural singularities due to its improper definition.

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“…We take ε=10 −3 . The fidelity susceptibility is found to be able to detect both the quantum critical point (χ F =+∞) and the EP (χ F =−∞) [38,39]. As shown in Fig.…”

Section: −F (γ)mentioning

confidence: 87%

Rényi entropies and negative central charges in non-Hermitian quantum systems

Tzeng

Chang

2022

SciPost Phys.

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“…However, the influence of the EPs may still be felt. Tzeng et al [26,27] describe how EPs in non-Hermitian systems can be detected precisely from numerical data by computing the fidelity susceptibility. They define a generalised fidelity for non-Hermitian systems as…”

Section: Exceptional Points and Positive Real λmentioning

confidence: 99%

Exceptional Points in the Baxter-Fendley Free Parafermion Model

Henry¹,

Batchelor²

2023

Preprint

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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 simple generalisation of this idea to Z N -symmetric models. In 1989 Baxter discovered a non-Hermitian but PT -symmetric model directly generalising the Ising chain which was much later recognised by Fendley to be a free parafermion spectrum. By extending the model's magnetic field parameter to the complex plane, we show 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 PT -symmetric at these exceptional points, their proximity can have a profound impact on the model on the PT -symmetric real line. Furthermore, in certain cases an exceptional point may appear on the real line (with negative field). Contents 5 Other Degeneracies of H 11 6 Exceptional Points and Positive Real λ 11 7 Conclusion 12

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“…As a purely geometric measure of quantum states, fidelity susceptibility is believed to be effective in characterizing sudden changes in ground-state structure associated with quantum phase transitions, and over the past few years this concept has been established as one of the powerful diagnostics methods for quantum phase transitions without prior knowledge of order parameters or associated symmetry-breaking patterns. To date, fidelity susceptibility has been applied to detect various quantum critical points, such as conventional symmetry-breaking quantum critical points (e.g.Ising critical point) [54,55], topological phase transitions [56], Anderson transitions [57,58], deconfined quantum criticality [59], and even non-Hermitian critical points [60][61][62]. In this work, we will show that this concept could also be an attractive tool for studying challenging C-IC problems.…”

Section: Introductionmentioning

confidence: 96%

Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain

Yu¹,

Yang²,

Xu³

et al. 2022

Preprint

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In recent years, programmable Rydberg atom arrays have been widely used to simulate new quantum phases and phase transitions, generating great interest among theorists and experimentalists. Based on the large-scale density matrix renormalization group method, the ground-state phase diagram of one-dimensional Rydberg chains is investigated with fidelity susceptibility as an efficient diagnostic method. We find that the competition between Rydberg blockade and external detuning produces unconventional phases and phase transitions. As the Rydberg blockade radius increases, the phase transition between disordered and period-3 density-wave ordered phases changes from the standard three-state Potts to the unconventional chiral universality class. As the radius increases further, a very narrow intermediate floating phase begins to appear. This result provides a concise physical picture to illustrate the numerical results. Compared with previous studies, this work provides more evidence for non-conformal quantum phase transitions in programmable quantum simulators from the perspective of quantum information, showing that fidelity susceptibility can be used to study commensurate-incommensurate phase transitions.

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

Cited by 3 publications

References 63 publications

Rényi entropies and negative central charges in non-Hermitian quantum systems

Rényi entropies and negative central charges in non-Hermitian quantum systems

Exceptional Points in the Baxter-Fendley Free Parafermion Model

Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain

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