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  • Letter
  • Open Access

Non-Hermitian many-body topological excitations in interacting quantum dots

Timo Hyart1,2 and J. L. Lado1

  • 1Department of Applied Physics, Aalto University, 00076 Aalto, Espoo, Finland
  • 2International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland

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Phys. Rev. Research 4, L012006 – Published 28 January, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L012006

Abstract

Quantum dots are one of the paradigmatic solid-state systems for quantum engineering, providing an outstanding tunability to explore fundamental quantum phenomena. Here we show that non-Hermitian many-body topological modes can be realized in a quantum dot chain by utilizing a gate-tunable modulation of dissipation, and they emerge purely because of the non-Hermiticity. By exactly solving the non-Hermitian interacting description both with exact diagonalization and tensor networks, we demonstrate that these topological modes are robust even in the presence strong interactions, leading to a strongly correlated topological many-particle state. Our results put forward quantum dot arrays as a platform for engineering non-Hermitian many-body topological modes, and highlight the resilience of non-Hermitian topology to electronic interactions.

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References (57)

  1. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  2. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  3. R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys. 14, 11 (2018).
  4. F. Song, S. Yao, and Z. Wang, Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems, Phys. Rev. Lett. 123, 170401 (2019).
  5. S. Lieu, M. McGinley, and N. R. Cooper, Tenfold Way for Quadratic Lindbladians, Phys. Rev. Lett. 124, 040401 (2020).
  6. K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Symmetry and Topology in Non-Hermitian Physics, Phys. Rev. X 9, 041015 (2019).
  7. P. M. Vecsei, M. M. Denner, T. Neupert, and F. Schindler, Symmetry indicators for inversion-symmetric non-Hermitian topological band structures, Phys. Rev. B 103, L201114 (2021).
  8. K. Sponselee, L. Freystatzky, B. Abeln, M. Diem, B. Hundt, A. Kochanke, T. Ponath, B. Santra, L. Mathey, K. Sengstock, and C. Becker, Dynamics of ultracold quantum gases in the dissipative Fermi-Hubbard model, Quantum Sci. Technol. 4, 014002 (2018).
  9. S. H. Cantu, A. V. Venkatramani, W. Xu, L. Zhou, B. Jelenković, M. D. Lukin, and V. Vuletić, Repulsive photons in a quantum nonlinear medium, Nat. Phys. 16, 921 (2020).
  10. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  11. J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, and A. Szameit, Observation of a Topological Transition in the Bulk of a Non-Hermitian System, Phys. Rev. Lett. 115, 040402 (2015).
  12. C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, Selective enhancement of topologically induced interface states in a dielectric resonator chain, Nat. Commun. 6, 6710 (2015).
  13. X. Zhan, L. Xiao, Z. Bian, K. Wang, X. Qiu, B. C. Sanders, W. Yi, and P. Xue, Detecting Topological Invariants in Nonunitary Discrete-Time Quantum Walks, Phys. Rev. Lett. 119, 130501 (2017).
  14. L. Xiao, X. Zhan, Z. H. Bian, K. K. Wang, X. Zhang, X. P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, and P. Xue, Observation of topological edge states in parity-time-symmetric quantum walks, Nat. Phys. 13, 1117 (2017).
  15. S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. Rechtsman, and A. Szameit, Topologically protected bound states in photonic parity-time-symmetric crystals, Nat. Mater. 16, 433 (2017).
  16. H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, and L. Feng, Topological hybrid silicon microlasers, Nat. Commun. 9, 981 (2018).
  17. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018).
  18. M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Edge-Mode Lasing in 1D Topological Active Arrays, Phys. Rev. Lett. 120, 113901 (2018).
  19. T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. W. Molenkamp, C. H. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys. 16, 747 (2020).
  20. D. I. Pikulin and Y. V. Nazarov, Topological properties of superconducting junctions, JETP Lett. 94, 693 (2012).
  21. D. I. Pikulin and Y. V. Nazarov, Two types of topological transitions in finite Majorana wires, Phys. Rev. B 87, 235421 (2013).
  22. S. Mi, D. I. Pikulin, M. Marciani, and C. W. J. Beenakker, X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot, J. Exp. Theor. Phys. 119, 1018 (2014).
  23. P. San-Jose, J. Cayao, E. Prada, and R. Aguado, Majorana bound states from exceptional points in non-topological superconductors, Sci. Rep. 6, 21427 (2016).
  24. J. Avila, F. Peñaranda, E. Prada, P. San-Jose, and R. Aguado, Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy, Commun. Phys. 2, 133 (2019).
  25. E. J. Bergholtz and J. C. Budich, Non-Hermitian Weyl physics in topological insulator ferromagnet junctions, Phys. Rev. Research 1, 012003(R) (2019).
  26. D. Ferry, R. Akis, A. Burke, I. Knezevic, R. Brunner, J. Bird, R. Meisels, F. Kuchar, and J. Bird, Open quantum dots: Physics of the non-Hermitian Hamiltonian, Fortschr. Phys. 61, 291 (2012).
  27. L.-L. Zhang, G.-H. Zhan, D.-Q. Yu, and W.-J. Gong, Transport through a non-Hermitian parallel double-quantum-dot structure in the presence of interdot Coulomb interaction, Superlattices Microstruct. 113, 558 (2018).
  28. T. Hensgens, T. Fujita, L. Janssen, X. Li, C. J. Van Diepen, C. Reichl, W. Wegscheider, S. Das Sarma, and L. M. K. Vandersypen, Quantum simulation of a Fermi-Hubbard model using a semiconductor quantum dot array, Nature (London) 548, 70 (2017).
  29. A. R. Mills, D. M. Zajac, M. J. Gullans, F. J. Schupp, T. M. Hazard, and J. R. Petta, Shuttling a single charge across a one-dimensional array of silicon quantum dots, Nat. Commun. 10, 1063 (2019).
  30. P.-A. Mortemousque, B. Jadot, E. Chanrion, V. Thiney, C. Bäuerle, A. Ludwig, A. D. Wieck, M. Urdampilleta, and T. Meunier, Enhanced spin coherence while displacing electron in a 2D array of quantum dots, PRX Quantum 2, 030331 (2021).
  31. I. C. Fulga, A. Haim, A. R. Akhmerov, and Y. Oreg, Adaptive tuning of Majorana fermions in a quantum dot chain, New J. Phys. 15, 045020 (2013).
  32. K. Takata and M. Notomi, Photonic Topological Insulating Phase Induced Solely by Gain and Loss, Phys. Rev. Lett. 121, 213902 (2018).
  33. W. Brzezicki and T. Hyart, Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems, Phys. Rev. B 100, 161105(R) (2019).
  34. P. Comaron, V. Shahnazaryan, W. Brzezicki, T. Hyart, and M. Matuszewski, Non-Hermitian topological end-mode lasing in polariton systems, Phys. Rev. Research 2, 022051(R) (2020).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L012006 for more details related to analytical results in the non-interacting limit, topological invariant, derivation of the non-Hermitian self-energy, end state wave functions and local correlator in the absence of interactions, tunneling conductance, models for topological phases with arbitrary large Chern number, and robustness of the topological end modes in the presence of interactions.
  36. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405 (1982).
  37. C. W. J. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys. 69, 731 (1997).
  38. S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2013).
  39. H. Bruus and K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics: An Introduction, Oxford Graduate Texts (Oxford University Press, Oxford, 2016).
  40. M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor software library for tensor network calculations, arXiv:2007.14822.
  41. ITensor Library, http://itensor.org.
  42. DMRGpy Library, https://github.com/joselado/dmrgpy.
  43. W. E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Q. Appl. Math. 9, 17 (1951).
  44. R. B. Lehoucq and D. C. Sorensen, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl. 17, 789 (1996).
  45. F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Rev. 43, 235 (2001).
  46. A. Stathopoulos, Y. Saad, and K. Wu, Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods, SIAM J. Sci. Comput. 19, 227 (1998).
  47. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, Philadelphia, 1998).
  48. L. Fidkowski and A. Kitaev, Effects of interactions on the topological classification of free fermion systems, Phys. Rev. B 81, 134509 (2010).
  49. L. Fidkowski and A. Kitaev, Topological phases of fermions in one dimension, Phys. Rev. B 83, 075103 (2011).
  50. C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  51. G. E. Volovik, Topological invariant for superfluid 3He-B and quantum phase transitions, JETP Lett. 90, 587 (2009).
  52. V. Gurarie, Single-particle Green's functions and interacting topological insulators, Phys. Rev. B 83, 085426 (2011).
  53. Z. Wang and S.-C. Zhang, Simplified Topological Invariants for Interacting Insulators, Phys. Rev. X 2, 031008 (2012).
  54. Z. Wang and B. Yan, Topological Hamiltonian as an exact tool for topological invariants, J. Phys.: Condens. Matter 25, 155601 (2013).
  55. T. Mertz, K. Zantout, and R. Valentí, Statistical analysis of the Chern number in the interacting Haldane-Hubbard model, Phys. Rev. B 100, 125111 (2019).
  56. D. Lessnich, S. M. Winter, M. Iraola, M. G. Vergniory, and R. Valentí, Elementary band representations for the single-particle Green's function of interacting topological insulators, Phys. Rev. B 104, 085116 (2021).
  57. Y.-Z. You, Z. Wang, J. Oon, and C. Xu, Topological number and fermion Green's function for strongly interacting topological superconductors, Phys. Rev. B 90, 060502(R) (2014).

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Phys. Rev. Research 4, L012006– Published 28 January, 2022
  • Received 12 July 2021
  • Accepted 11 January 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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