Conventional quantum phase transition driven by a complex parameter in a non-Hermitian<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi><mml:mo>−</mml:mo><mml:mi>symmetric</mml:mi></mml:math>Ising model

Li, C.; Zhang, G.; Zhang, X. Z.; Song, Z.

doi:10.1103/physreva.90.012103

Cited by 39 publications

(18 citation statements)

References 41 publications

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“…In recent years there has been growing interest in non-Hermitian PT -symmetric Hamiltonian systems (for a recent review, see [2] and references therein). Examples of such systems range from quantum field theories [3] to open quantum systems [4], the Anderson models [5][6][7], the tightbinding chain [8][9][10][11], the spin chain [12,13] and topological models [14,15], as well as the optical systems [16][17][18][19][20][21]. Moreover, crucial advances in photonic lattices and photonic crystals have made it possible to experimentally implement non-Hermitian PT -symmetric systems [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 98%

SpontaneousPT-symmetry breaking in non-Hermitian Kitaev and extended Kitaev models

et al. 2015

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The spontaneous parity-time (PT ) symmetry breaking is discussed in non-Hermitian PT -symmetric Kitaev and extended Kitaev models whose Hermiticity is broken by the presence of two conjugated imaginary potentials ±iγ at two end sites. In the case of the non-Hermitian Kitaev model, a spontaneous PT -symmetry breaking transition (SPT BT ) occurs at a certain γ c in the topologically trivial phase (TTP) region, similar to that of the Su-Schrieffer-Heeger (SSH) model. However, unlike the SSH model, the system also undergoes such a transition in the topologically nontrivial phase (TNP) region. We study an extended Kitaev model by combining the superconducting pairing in the Kitaev model and the staggered hopping in the SSH model. This model contains three different topological phases: the TTP, the Kitaev-like TNP, and the SSH-like TNP. For the non-Hermitian extended Kitaev model, a SPT BT occurs in the Kitaev-like TNP region, as well as in part of the TTP and SSH-like TNP regions, whereas the PT symmetry is broken for an arbitrary nonzero γ in the rest of the TTP and SSH-like TNP regions. Therefore, we can conclude that there is no universal correlation between topological properties and the SPT BT .

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Section: Introductionmentioning

confidence: 98%

SpontaneousPT-symmetry breaking in non-Hermitian Kitaev and extended Kitaev models

et al. 2015

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“…Transport, localization and scattering of quantum or classical waves in systems described by effective non-Hermitian Hamiltonians are of major interest in different areas of science , ranging from the physics of open quantum systems to mesoscopic solid-state structures [2,13,14,17,20,23,25], atomic and molecular physics [1,34], optics and photonics [18,29,31,36,37,39,40,43], acoustics [48,52], magnetic and spin systems [21,28,32,33,35,46,47], quantum computing [26,27,42], and biological systems [7,50]. Several important signatures of non-Hermitian transport have been revealed, including non-Hermitian delocalization in disordered lattices [3][4][5][6][7][8][9][10][11][12], one-way scattering [15,16], transition from ballistic to diffusive transport [29], hyperballistic transport [30], invisibility of defects…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian bidirectional robust transport

Longhi

2017

Phys. Rev. B

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Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-enviroment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996)], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically-protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the HatanoNelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

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“…Many new physical phenomena have been proposed based on pseudo-Hermiticity. For example, the real spectra in non-Hermitian topological insulators [14], quantum phase transitions [15][16][17], Goldstones theorem [18], PT -symmetric quantum walks [19] and quantum sensing [20]. In the following of our analysis, the pseudo-Hermiticity we considered excludes both the Hermiticity and the PT -symmetry.…”

Section: Introductionmentioning

confidence: 99%

High-order exceptional point in a nanofiber cavity quantum electrodynamics system

Li¹,

Li²,

Zhang³

2022

Preprint

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We present an all-fiber emitter-cavity quantum electrodynamics (QED) system which consists of two twolevel emitters and a nanofiber cavity. Our scheme makes it possible to observe the higher-order exceptional points based on the coupling between the emitters and the nanofiber cavity. The effective gain of this cavity can be obtained by weakly driven to the nanofiber cavity via two identical laser fields, which will realize coherent perfect absorption (CPA) in the implementation of the experiments. Under the experimental feasible parameters, the Hamiltonian of this system is in the condition of pseudo-Hermiticity, which means that its eigenvalues can be made of one real and a pair of complex conjugates, or be all real. By controllably tuned the ratio of the two emitter-cavity coupling strengths, and the ratio of the decay rates of the emitters, we can discover both the three-order exceptional point (EP3) and the second-order exceptional point (EP2) without parity-time symmetry in our emitter-cavity system. These results can also be demonstrated by the total output spectra and transmission spectra. We also find that the symmetric modes come into being when the coupling strength greater than the critical coupling strength at EP3 points. Our proposal will provide a new method to realize higher-order exceptional points based on the quantum network.

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Conventional quantum phase transition driven by a complex parameter in a non-HermitianPT−symmetricIsing model

Cited by 39 publications

References 41 publications

SpontaneousPT-symmetry breaking in non-Hermitian Kitaev and extended Kitaev models

SpontaneousPT-symmetry breaking in non-Hermitian Kitaev and extended Kitaev models

Non-Hermitian bidirectional robust transport

High-order exceptional point in a nanofiber cavity quantum electrodynamics system

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