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  • Letter

Bridging the gap between topological non-Hermitian physics and open quantum systems

Álvaro Gómez-León, Tomás Ramos, Alejandro González-Tudela, and Diego Porras
Phys. Rev. A 106, L011501 – Published 25 July 2022
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    Abstract

    We relate observables in open quantum systems with the topology of non-Hermitian models using the Keldysh path-integral method. This allows to extract an effective Hamiltonian from the Green's function which contains all the relevant topological information and produces ω-dependent topological invariants, linked to the response functions at a given frequency. Then, we show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a one-dimensional Hatano-Nelson model, highlighting the difference between the bosonic and the fermionic case.

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    • Received 28 September 2021
    • Revised 1 February 2022
    • Accepted 1 July 2022

    DOI:https://doi.org/10.1103/PhysRevA.106.L011501

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    BosonsFermionsPhotonicsQuantum opticsSkin effectTopological insulatorsTopological materialsTopological phase transitionTopological phases of matter
    Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Álvaro Gómez-León*, Tomás Ramos†, Alejandro González-Tudela‡, and Diego Porras§

    • Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain

    • *a.gomez.leon@csic.es
    • †t.ramos.delrio@gmail.com
    • ‡a.gonzalez.tudela@csic.es
    • §diego.porras@csic.es

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    Issue

    Vol. 106, Iss. 1 — July 2022

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    Images

    • Figure 1
      Figure 1

      (Left) Schematic for the H-N model. Sites in the array coherently couple with hopping tc and auxiliary sites are dissipatively coupled via κ and td. (Right) Complex plane plot of the eigenvalues of HR for the bosonic (red) and the fermionic (blue) H-N model with periodic boundary conditions (PBCs). The fermionic case never encloses the origin and remains trivial. Red and blue dots show the collapse of the eigenvalues due to the skin effect for open boundary conditions (OBCs).

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    • Figure 2
      Figure 2

      (Top) W1(ω) for different values of κ/td. In the fermionic case W1(ω) is always zero (blue). (Middle) Eigenvalues of H̃ vs ω for κ/td=4. The spectrum for PBCs is shown in red, whereas black dots indicate the two boundary modes with OBCs. (Bottom) Eigenvalues of H̃ vs k for κ/td=4 and ω/td=2. All plots consider tc/td=1 and ϕ=π/2

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    • Figure 3
      Figure 3

      Logarithmic scale plot of χjl(ω) between sites l=1 and j=2,4,6,8,and10. We have considered the bosonic case for an array with N=10 sites, tc/td=1 and ϕ=π/2. The crossing at a certain value of ω allows to extract the position of the critical point, indicated for the cases of κ/td=4and7.

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