Topological edge states of the 
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-symmetric Su-Schrieffer-Heeger model: An effective two-state description

Tzortzakakis, A. F.; A., Katsaris,; Palaiodimopoulos, N. E.; Kalozoumis, P. A.; Theocharis, G.; Diakonos, F. K.; Petrosyan, David

doi:10.1103/physreva.106.023513

Cited by 14 publications

(3 citation statements)

References 46 publications

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“…For convenience, we denote the three chains by L, R, and M, according to their locations in the figure . Here, we consider cases where the three SSH chains have the same size N (N ∈ even) and the total number is L = 3N + 1. When we restrict ourselves to the one-excitation subspace, the Hamiltonian of this splicing Y-junction SSH chain is written as [27,34,35]…”

Section: Planar Qst With the Equal Probabilitiesmentioning

confidence: 99%

Planar and tunable quantum state transfer in a splicing Y-junction Su–Schrieffer–Heeger chain

Zheng,

Wang,

2023

New J. Phys.

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We present a feasible scheme to implement a planar and tunable quantum state transfer (QST) via topologically protected zero-energy mode in a splicing Y-junction Su-Schrieffer-Heeger (SSH) chain. The introduction of the elaborate nearest-neighbor hopping enables one to generate a topological interface at the central site of the Y-junction. By modulating the nearest-neighbor hopping adiabatically in the chain, the quantum state initially prepared at the central site can be simultaneously transferred to the three endpoints of the Y-junction with the equal/unequal probabilities. The planar distribution of QST is expected to realize a quantum router, whose function is to make the quantum information on the central site (input port) appear equally/unequally at the three endpoints (output ports) with different directions. Moreover, the numerical simulations demonstrate that the scheme possesses the robustness on the fluctuations of the nearest-neighbor hopping and the on-site potential in the system. Furthermore, we show that the number of the output ports with different directions can be flexibly increased in an extended X-junction SSH chain, and the experimental feasibility for implementing special QST in a superconducting qubit-resonator system is briefly discussed. Our work extends the space distribution of QST from linear distribution to planar distribution and promotes the construction of large-scale quantum networks.

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Section: Planar Qst With the Equal Probabilitiesmentioning

confidence: 99%

Planar and tunable quantum state transfer in a splicing Y-junction Su–Schrieffer–Heeger chain

Zheng,

Wang,

2023

New J. Phys.

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“…Many studies have recently shown that non-Hermitian systems have profound application value due to their many novel and unique topological properties in enhancing sensing [10][11][12], topological lasers [13], and topological optical funnels [14]. The most typical approach is gain and loss potential [15][16][17], or non reciprocal coupling [18][19][20].…”

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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“…A non-unitary but Hermitian transformation operator is formulated explicitly to convert the non-Hermitian Hamiltonian [36,47] to its Hermitian counterpart for the SU(1, 1) and SU(2) systems. The SU(1, 1) Hamiltonian has been well studied [48][49][50][51][52], while the Hermitian counterpart of SU(2) pseudo-Hermitian Hamiltonian has not been realized for a spin system of arbitrary spin-value j.…”

Section: Introductionmentioning

confidence: 99%

Generalized gauge transformation and the corresponding Hermitian counterparts of SU(1, 1), SU(2) pseudo-Hermitian Hamiltonians

Liu

Liang²,

Gu³

2023

Phys. Scr.

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We study in this paper both the stationary and time-dependent pseudo-Hermitian Hamiltonians consisting respectively of SU(1, 1), SU(2) generators. The pseudo-Hermitian Hamiltonians can be generated from kernel Hermitian-Hamiltonians by a generalized gauge transformation with a non-unitary but Hermitian operator. The metric operator of the biorthogonal sets of eigenstates is simply the square of the transformation operator, which is formulated explicitly. The exact solutions of pseudo-Hermitian Hamiltonians are obtained in terms of the eigenststates of the Hermitian counterparts. We observe a critical point Gc of coupling constant, where all eigenstates of the stationary Hamiltonians are degenerate with a vanishing eigenvalue. This critical point is modified as Gc(ω) in the time-dependent case including the frequency of external field. Returning to the original gauge we obtain analytically the wave functions and associated non-adiabatic Berry phase, which diverges at the critical point for the SU(2) Hamiltonian. Beyond the critical point Berry phase becomes a complex domain.

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Topological edge states of the PT -symmetric Su-Schrieffer-Heeger model: An effective two-state description

Cited by 14 publications

References 46 publications

Planar and tunable quantum state transfer in a splicing Y-junction Su–Schrieffer–Heeger chain

Planar and tunable quantum state transfer in a splicing Y-junction Su–Schrieffer–Heeger chain

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

Generalized gauge transformation and the corresponding Hermitian counterparts of SU(1, 1), SU(2) pseudo-Hermitian Hamiltonians

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