Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Controlled buildup of half-quantized thermal conductance in an engineered chiral spin liquid platform

Bo-Ye Sun1,*, Baptiste Bermond2, Lucila Peralta Gavensky3,4, Marin Bukov5, Zheng-Wei Zhou6, and Nathan Goldman2,3,4

  • *Contact author: boyesun@ytu.edu.cn

Phys. Rev. Research 8, 023226 – Published 29 May, 2026

DOI: https://doi.org/10.1103/wbvr-9z8t

Abstract

We study thermal transport along the edge of a small chiral spin liquid device coupled to two Ising-chain reservoirs, a platform suitable for quantum-engineered systems. Adiabatically switching on the tunnel couplings to the reservoirs generates a thermal current that dynamically builds up and reaches a quasi-steady-state regime. In this experimentally critical time window, the two-terminal thermal conductance can approach half-quantized values—a hallmark of Majorana-mediated transport—under finely tuned conditions. The results agree with an effective Landauer-Büttiker description in the large-reservoir limit, where energy-resolved transmission rates help identify the optimal parameters to achieve the half-quantized conductance. This work provides a controllable platform to investigate topological thermal transport in engineered spin systems, such as realized in cold-atom and Rydberg-atom settings.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (69)

  1. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (NY) 321, 2 (2006).
  2. G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, et al., Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021).
  3. K. Satzinger, Y.-J. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, et al., Realizing topologically ordered states on a quantum processor, Science 374, 1237 (2021).
  4. S. Xu, Z.-Z. Sun, K. Wang, L. Xiang, Z. Bao, Z. Zhu, F. Shen, Z. Song, P. Zhang, W. Ren, et al., Digital simulation of non-Abelian anyons with 68 programmable superconducting qubits, Chin. Phys. Lett. 40, 060301 (2023).
  5. S. Zhou, M. Zelenayova, O. Hart, C. Chamon, and C. Castelnovo, Probing fractional statistics in quantum simulators of spin liquid Hamiltonians, SciPost Phys. 15, 194 (2022).
  6. S. Trebst and C. Hickey, Kitaev materials, Phys. Rep. 950, 1 (2022).
  7. M. Hermanns, I. Kimchi, and J. Knolle, Physics of the Kitaev model: Fractionalization, dynamic correlations, and material connections, Annu. Rev. Condens. Matter Phys. 9, 17 (2018).
  8. J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
  9. H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Concept and realization of Kitaev quantum spin liquids, Nat. Rev. Phys. 1, 264 (2019).
  10. B.-Y. Sun, N. Goldman, M. Aidelsburger, and M. Bukov, Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms, PRX Quantum 4, 020329 (2023).
  11. A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).
  12. A. Stern and N. H. Lindner, Topological quantum computation—From basic concepts to first experiments, Science 339, 1179 (2013).
  13. Google Quantum AI and Collaborators, Non-Abelian braiding of graph vertices in a superconducting processor, Nature (London) 618, 264 (2023).
  14. Y. D. Lensky, K. Kechedzhi, I. Aleiner, and E.-A. Kim, Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code, Ann. Phys. (NY) 452, 169286 (2023).
  15. N. Harle, O. Shtanko, and R. Movassagh, Observing and braiding topological Majorana modes on programmable quantum simulators, Nat. Commun. 14, 2286 (2023).
  16. J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, Dynamics of a two-dimensional quantum spin liquid: Signatures of emergent Majorana fermions and fluxes, Phys. Rev. Lett. 112, 207203 (2014).
  17. J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, Dynamics of fractionalization in quantum spin liquids, Phys. Rev. B 92, 115127 (2015).
  18. M. Schmitt and S. Kehrein, Dynamical quantum phase transitions in the Kitaev honeycomb model, Phys. Rev. B 92, 075114 (2015).
  19. A. Banerjee, J. Yan, J. Knolle, C. A. Bridges, M. B. Stone, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, R. Moessner, and S. E. Nagler, Neutron scattering in the proximate quantum spin liquid α−RuCl3, Science 356, 1055 (2017).
  20. A. Smith, J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, Majorana spectroscopy of three-dimensional Kitaev spin liquids, Phys. Rev. B 93, 235146 (2016).
  21. J.-Y. Chen, L. Vanderstraeten, S. Capponi, and D. Poilblanc, Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study, Phys. Rev. B 98, 184409 (2018).
  22. J. Feldmeier, W. Natori, M. Knap, and J. Knolle, Local probes for charge-neutral edge states in two-dimensional quantum magnets, Phys. Rev. B 102, 134423 (2020).
  23. T. Mizoguchi, T. Koma, and Y. Yoshida, Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models, Phys. Rev. B 101, 014442 (2020).
  24. N. Li, X. Zhao, and X.-F. Sun, Ultralow-temperature heat transport in quantum spin liquid candidates: A brief review, Chin. Phys. Lett. 41, 127501 (2024).
  25. H. Zou and W. Wang, Gapless spin liquid and nonlocal corner excitation in the spin-1/2 Heisenberg antiferromagnet on fractal, Chin. Phys. Lett. 40, 057501 (2023).
  26. U. Roy, S. Manna, S. Chakraborty, K. Watanabe, T. Taniguchi, A. Das, M. Goldstein, Y. Gefen, and A. Das, Half-integer thermal conductance in the absence of Majorana mode, Nat. Commun. 17, 2853 (2025).
  27. J. Nasu, J. Yoshitake, and Y. Motome, Thermal transport in the Kitaev model, Phys. Rev. Lett. 119, 127204 (2017).
  28. A. P. Joy and A. Rosch, Dynamics of visons and thermal Hall effect in perturbed Kitaev models, Phys. Rev. X 12, 041004 (2022).
  29. Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, et al., Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid, Nature (London) 559, 227 (2018).
  30. J. Bruin, R. Claus, Y. Matsumoto, N. Kurita, H. Tanaka, and H. Takagi, Robustness of the thermal Hall effect close to half-quantization in α−RuCl3, Nat. Phys. 18, 401 (2022).
  31. M. Yamashita, J. Gouchi, Y. Uwatoko, N. Kurita, and H. Tanaka, Sample dependence of half-integer quantized thermal Hall effect in the Kitaev spin-liquid candidate α−RuCl3, Phys. Rev. B 102, 220404(R) (2020).
  32. N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nat. Phys. 12, 639 (2016).
  33. N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019).
  34. J. Léonard, S. Kim, J. Kwan, P. Segura, F. Grusdt, C. Repellin, N. Goldman, and M. Greiner, Realization of a fractional quantum Hall state with ultracold atoms, Nature (London) 619, 495 (2023).
  35. S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms, Science 365, 775 (2019).
  36. R. Verresen, M. D. Lukin, and A. Vishwanath, Prediction of toric code topological order from Rydberg blockade, Phys. Rev. X 11, 031005 (2021).
  37. Y.-H. Chen, B.-Z. Wang, T.-F. J. Poon, X.-C. Zhou, Z.-X. Liu, and X.-J. Liu, Proposal for realization and detection of Kitaev quantum spin liquid with Rydberg atoms, Phys. Rev. Res. 6, L042054 (2024).
  38. M. Kalinowski, N. Maskara, and M. D. Lukin, Non-Abelian Floquet spin liquids in a digital Rydberg simulator, Phys. Rev. X 13, 031008 (2023).
  39. S. J. Evered, M. Kalinowski, A. A. Geim, T. Manovitz, D. Bluvstein, S. H. Li, N. Maskara, H. Zhou, S. Ebadi, M. Xu, J. Campo, M. Cain, S. Ostermann, S. F. Yelin, S. Sachdev, M. Greiner, V. Vuletić, and M. D. Lukin, Probing the Kitaev honeycomb model on a neutral-atom quantum computer, Nature (London) 645, 341 (2025).
  40. M. Will, T. A. Cochran, E. Rosenberg, B. Jobst, N. M. Eassa, P. Roushan, M. Knap, A. Gammon-Smith, and F. Pollmann, Probing non-equilibrium topological order on a quantum processor, Nature (London) 645, 348 (2025).
  41. J. Wu, L. Zhu, and Q. Si, Crossovers and critical scaling in the one-dimensional transverse-field Ising model, Phys. Rev. B 97, 245127 (2018).
  42. V. Borish, O. Marković, J. A. Hines, S. V. Rajagopal, and M. Schleier-Smith, Transverse-field Ising dynamics in a Rydberg-dressed atomic gas, Phys. Rev. Lett. 124, 063601 (2020).
  43. P. Pfeuty, The one-dimensional Ising model with a transverse field, Ann. Phys. (NY) 57, 79 (1970).
  44. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, Heidelberg, 2008).
  45. S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge Studies in Semiconductor Physics and Microelectronic Engineering (Cambridge University Press, Cambridge, UK, 1995).
  46. A. Kundu and B. Seradjeh, Transport signatures of Floquet Majorana fermions in driven topological superconductors, Phys. Rev. Lett. 111, 136402 (2013).
  47. A. Farrell and T. Pereg-Barnea, Photon-inhibited topological transport in quantum well heterostructures, Phys. Rev. Lett. 115, 106403 (2015).
  48. H. H. Yap, L. Zhou, J.-S. Wang, and J. Gong, Computational study of the two-terminal transport of Floquet quantum Hall insulators, Phys. Rev. B 96, 165443 (2017).
  49. G. Salerno, H. M. Price, M. Lebrat, S. Häusler, T. Esslinger, L. Corman, J.-P. Brantut, and N. Goldman, Quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions, Phys. Rev. X 9, 041001 (2019).
  50. X.-Y. Feng, G.-M. Zhang, and T. Xiang, Topological characterization of quantum phase transitions in a spin-1/2 model, Phys. Rev. Lett. 98, 087204 (2007).
  51. H.-D. Chen and J. Hu, Exact mapping between classical and topological orders in two-dimensional spin systems, Phys. Rev. B 76, 193101 (2007).
  52. H.-D. Chen and Z. Nussinov, Exact results of the Kitaev model on a hexagonal lattice: Spin states, string and brane correlators, and anyonic excitations, J. Phys. A: Math. Theor. 41, 075001 (2008).
  53. H. Sumiyoshi and S. Fujimoto, Quantum thermal Hall effect in a time-reversal-symmetry-broken topological superconductor in two dimensions: Approach from bulk calculations, J. Phys. Soc. Jpn. 82, 023602 (2013).
  54. S. Krinner, D. Stadler, D. Husmann, J.-P. Brantut, and T. Esslinger, Observation of quantized conductance in neutral matter, Nature (London) 517, 64 (2015).
  55. S. Krinner, M. Lebrat, D. Husmann, C. Grenier, J. P. Brantut, and T. Esslinger, Mapping out spin and particle conductances in a quantum point contact, Proc. Natl. Acad. Sci. USA 113, 8144 (2016).
  56. S. Krinner, T. Esslinger, and J.-P. Brantut, Two-terminal transport measurements with cold atoms, J. Phys.: Condens. Matter 29, 343003 (2017).
  57. L. Amico, D. Anderson, M. Boshier, J.-P. Brantut, L.-C. Kwek, A. Minguzzi, and W. von Klitzing, Colloquium: Atomtronic circuits: From many-body physics to quantum technologies, Rev. Mod. Phys. 94, 041001 (2022).
  58. P. T. Brown, D. Mitra, E. Guardado-Sanchez, R. Nourafkan, A. Reymbaut, C.-D. Hebert, S. Bergeron, A.-M. S. Tremblay, J. Kokalj, D. A. Huse, P. Schaub, and W. S. Bakr, Bad metallic transport in a cold atom Fermi-Hubbard system, Science 363, 379 (2019).
  59. Y.-H. Wan and Q.-F. Sun, Quarter-quantized thermal Hall effect with parity anomaly, Phys. Rev. B 109, 195408 (2024).
  60. Q. Yan, H. Li, J. Zeng, Q.-F. Sun, and X. C. Xie, A Majorana perspective on understanding and identifying axion insulators, Commun. Phys. 4, 239 (2021).
  61. Y. Huang, F. Setiawan, and J. D. Sau, Disorder-induced half-integer quantized conductance plateau in quantum anomalous Hall insulator-superconductor structures, Phys. Rev. B 97, 100501(R) (2018).
  62. L. Arrachea, G. S. Lozano, and A. A. Aligia, Thermal transport in one-dimensional spin heterostructures, Phys. Rev. B 80, 014425 (2009).
  63. M. Łącki, H. Pichler, A. Sterdyniak, A. Lyras, V. E. Lembessis, O. Al-Dossary, J. C. Budich, and P. Zoller, Quantum Hall physics with cold atoms in cylindrical optical lattices, Phys. Rev. A 93, 013604 (2016).
  64. The fluctuations of the orange signal lack perfect symmetry, which is expected, as it takes time for variations in one reservoir to propagate to the other.
  65. L. Peralta Gavensky, G. Usaj, and C. A. Balseiro, Nonequilibrium edge transport in quantum Hall based Josephson junctions, Phys. Rev. B 103, 024527 (2021).
  66. Q. Niu, D. J. Thouless, and Y.-S. Wu, Quantized Hall conductance as a topological invariant, Phys. Rev. B 31, 3372 (1985).
  67. N. Goldman and T. Ozawa, Relating the Hall conductivity to the many-body Chern number using Fermi's golden rule and Kramers-Kronig relations, C. R. Phys. 25, 289 (2024).
  68. I. C. Fulga, Y. Oreg, A. D. Mirlin, A. Stern, and D. F. Mross, Temperature enhancement of thermal Hall conductance quantization, Phys. Rev. Lett. 125, 236802 (2020).
  69. B.-Y. Sun, Controlled buildup of half-quantized thermal conductance in an engineered chiral spin liquid platform [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.20234596.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation