Spontaneous<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetry breaking in non-Hermitian Kitaev and extended Kitaev models

Wang, Xiaohui; Liu, Tingting; Xiong, Ye; Tong, Peiqing

doi:10.1103/physreva.92.012116

Cited by 83 publications

(61 citation statements)

References 49 publications

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“…In parallel, non-Hermitian physics exhibits considerable intriguing features ; the unexpected novel interface states appear between non-Hermitian periodic media with distinct topologies [76][77][78][79][80][81][82][83][84][85][86][87][88][89]. These stimulate the studies of topological phases and edge states in non-Hermitian systems .…”

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confidence: 99%

Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry

2019

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Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological phase transition. However, the way of non-Hermiticity appearance may alter the system topology. By alternatively introducing the non-Hermiticity under symmetry to prevent nonzero imaginary magnetic flux, the bulk-boundary correspondence recovers and every bulk state becomes extended; the bulk topology of Bloch Hamiltonian predicts the (non)existence of edge states and topological phase transition. These are elucidated in a non-Hermitian Su-Schrieffer-Heeger model, where chiral-inversion symmetry ensures the vanishing of imaginary magnetic flux. The average value of Pauli matrices under the eigenstate of chiralinversion symmetric Bloch Hamiltonian defines a vector field, the vorticity of topological defects in the vector field is a topological invariant. Our findings are applicable in other non-Hermitian systems. We first uncover the roles played by non-Hermitian AB effect and chiral-inversion symmetry for the breakdown and recovery of bulk-boundary correspondence, and develop new insights for understanding non-Hermitian topological phases of matter. arXiv:1809.03139v3 [cond-mat.mes-hall]

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confidence: 99%

Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry

2019

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“…With appropriate conditions, these PT -symmetric Hamiltonians can have purely real energy spectra [7,8]. The properties of PT -symmetric Hamiltonians and the corresponding breaking of this symmetry in many different non-Hermitian systems have been extensively studied [9][10][11][12][13][14][15][16][17][18][19]. Experimentally, there are also many different kinds of realizations of open systems in optical [20][21][22][23], mechanical [24], and electrical [25] setups, which endow the non-Hermitian Hamiltonians more practical signifi-cance.…”

Section: Introductionmentioning

confidence: 99%

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

2017

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We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

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“…Lower side: In this work we study dissipative extensions of the SSH model where sites marked with a plus (minus) sign indicate single-particle gain (loss). The two patterns with dissipation only among the boundary sites (U1, middle row) and alternating gain and loss (U2, bottom row) are motivated by previous works [5,14,16,17,28].…”

Section: Dissipative Frameworkmentioning

confidence: 98%

Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model

et al. 2018

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We investigate dissipative extensions of the Su-Schrieffer-Heeger model with regard to different approaches of modeling dissipation. In doing so, we use two distinct frameworks to describe the gain and loss of particles, one uses Lindblad operators within the scope of Lindblad master equations, the other uses complex potentials as an effective description of dissipation. The reservoirs are chosen in such a way that the non-Hermitian complex potentials are PT -symmetric. From the effective theory we extract a state which has similar properties as the non-equilibrium steady state following from Lindblad master equations with respect to lattice site occupation. We find considerable similarities in the spectra of the effective Hamiltonian and the corresponding Liouvillean. Further, we generalize the concept of the Zak phase to the dissipative scenario in terms of the Lindblad description and relate it to the topological phases of the underlying Hermitian Hamiltonian.

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

Cited by 83 publications

References 49 publications

Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry

Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

Topological invariants in dissipative extensions of the Su-Schrieffer-Heeger model

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