Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field

Nishiyama, Yoshihiro

doi:10.1140/epjb/e2020-10264-5

Cited by 7 publications

(6 citation statements)

References 40 publications

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“…The concept of fidelity susceptibility has been extended to non-Hermitian quantum systems. Due to the eigenvectors being labelled with left and right, many different definitions of fidelity were proposed [42][43][44][45][46][47][48][49][50]. In particular, the metricized fidelity is interestingly used for hunting for both quantum critical points and exceptional points [42].…”

Section: Introductionmentioning

confidence: 99%

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

Tu¹,

Jang²,

Chang³

et al. 2022

Preprint

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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 constrain of parity-time (PT) symmetry, we show that the fidelity F is always real for the PT-symmetric states. For the PT-broken states, the real part of the fidelity susceptibility equals to one half of the sum of the fidelity susceptibility of the PT-broken and the PT-partner states, Re[XF ] = 1 2 (XF + XF ). The negative infinity of the fidelity susceptibility is explored by the perturbation theory when the parameter approaches the exceptional point (EP). Moreover, at the second-order EP where two eigenstates and eigenenergies coalesce, we prove that the real part of the fidelity between PTsymmetric and PT-broken states is ReF = 1 2 . We demonstrate these general properties for noninteracting and interacting systems by two examples: the two-legged non-Hermitian Su-Schrieffer-Heeger (SSH) model and the non-Hermitian XXZ spin chain.

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Section: Introductionmentioning

confidence: 99%

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

Tu¹,

Jang²,

Chang³

et al. 2022

Preprint

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“…Many novel non-Hermitian phenomena have been detected, such as parity-time (PT ) symmetry [31][32][33], non-Hermitian skin effect [34,35], new topological behaviors associated with exceptional points [23,[36][37][38][39][40][41], disorder induced by non-Hermiticity [42][43][44], etc. Recently, intense attention has been paid on how non-Hermiticity influences quantum phase transitions in systems with rotation-time-reversal (RT ) symmetry [45][46][47][48], spin model with imaginary external field [49][50][51] and so on.…”

Section: Introductionmentioning

confidence: 99%

Emergent phase transition in Cluster Ising model with dissipation

Guo,

Yu,

et al. 2022

Preprint

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We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are tentatively located. String order parameter and staggered magnetization are then detected to reveal emergent phases of brand new characteristics. To categorize the exotic phases induced by non-Hermiticity, we calculate the variation mode of spin correlation function, which indicates the emergent critical points denote phase transitions without symmetry breaking. With the help of string order parameter and staggered magnetization, we find that there are four phases after introducing the non-Hermiticity-two symmetry-protected-topological (SPT) phases, one paramagnetic (PM) phase and one antiferromagnetic (AF) phase. A phase diagram is then presented to graphically illustrate the generation of three critical lines from a critical point as non-Hermitian strength increases, which correspond to SPT-SPT, SPT-PM and PM-AFM phase transition, respectively. Our theoretical work is expected to be realized in the experiment of ultracold atoms, pushing for progress in exploring novel topological phases and phase transitions.

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“…Fidelity (or fidelity susceptibility (FS)), a simple concept from quantum information, is widely used to detect quantum phase transitions in Hermitian many-body systems . Recently, the fidelity susceptibility has been generalized to the non-Hermitian systems to characterize non-Hermitian phase transitions [34,35,[86][87][88][89][90][91][92]. Because there exist two sets of eigenstates (left and right eigenstates) [93], one can define two types of fidelities depending on the usage of left and right eigenstates [38].…”

Section: Introductionmentioning

confidence: 99%

Biorthogonal quantum criticality in non-Hermitian many-body systems

2021

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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 the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a secondorder 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.

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Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field

Cited by 7 publications

References 40 publications

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

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

Emergent phase transition in Cluster Ising model with dissipation

Biorthogonal quantum criticality in non-Hermitian many-body systems

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