- Open Access
Controlled buildup of half-quantized thermal conductance in an engineered chiral spin liquid platform
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.
Physics Subject Headings (PhySH)
Article Text
References (69)
- A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (NY) 321, 2 (2006).
- 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).
- 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).
- 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).
- 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).
- S. Trebst and C. Hickey, Kitaev materials, Phys. Rep. 950, 1 (2022).
- 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).
- J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
- 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).
- 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).
- A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).
- A. Stern and N. H. Lindner, Topological quantum computation—From basic concepts to first experiments, Science 339, 1179 (2013).
- Google Quantum AI and Collaborators, Non-Abelian braiding of graph vertices in a superconducting processor, Nature (London) 618, 264 (2023).
- 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).
- N. Harle, O. Shtanko, and R. Movassagh, Observing and braiding topological Majorana modes on programmable quantum simulators, Nat. Commun. 14, 2286 (2023).
- 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).
- J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, Dynamics of fractionalization in quantum spin liquids, Phys. Rev. B 92, 115127 (2015).
- M. Schmitt and S. Kehrein, Dynamical quantum phase transitions in the Kitaev honeycomb model, Phys. Rev. B 92, 075114 (2015).
- 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 , Science 356, 1055 (2017).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- J. Nasu, J. Yoshitake, and Y. Motome, Thermal transport in the Kitaev model, Phys. Rev. Lett. 119, 127204 (2017).
- A. P. Joy and A. Rosch, Dynamics of visons and thermal Hall effect in perturbed Kitaev models, Phys. Rev. X 12, 041004 (2022).
- 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).
- J. Bruin, R. Claus, Y. Matsumoto, N. Kurita, H. Tanaka, and H. Takagi, Robustness of the thermal Hall effect close to half-quantization in , Nat. Phys. 18, 401 (2022).
- 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 , Phys. Rev. B 102, 220404(R) (2020).
- N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nat. Phys. 12, 639 (2016).
- N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019).
- 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).
- 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).
- R. Verresen, M. D. Lukin, and A. Vishwanath, Prediction of toric code topological order from Rydberg blockade, Phys. Rev. X 11, 031005 (2021).
- 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).
- M. Kalinowski, N. Maskara, and M. D. Lukin, Non-Abelian Floquet spin liquids in a digital Rydberg simulator, Phys. Rev. X 13, 031008 (2023).
- 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).
- 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).
- 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).
- 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).
- P. Pfeuty, The one-dimensional Ising model with a transverse field, Ann. Phys. (NY) 57, 79 (1970).
- H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, Heidelberg, 2008).
- S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge Studies in Semiconductor Physics and Microelectronic Engineering (Cambridge University Press, Cambridge, UK, 1995).
- A. Kundu and B. Seradjeh, Transport signatures of Floquet Majorana fermions in driven topological superconductors, Phys. Rev. Lett. 111, 136402 (2013).
- A. Farrell and T. Pereg-Barnea, Photon-inhibited topological transport in quantum well heterostructures, Phys. Rev. Lett. 115, 106403 (2015).
- 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).
- 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).
- X.-Y. Feng, G.-M. Zhang, and T. Xiang, Topological characterization of quantum phase transitions in a spin- model, Phys. Rev. Lett. 98, 087204 (2007).
- H.-D. Chen and J. Hu, Exact mapping between classical and topological orders in two-dimensional spin systems, Phys. Rev. B 76, 193101 (2007).
- 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).
- 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).
- S. Krinner, D. Stadler, D. Husmann, J.-P. Brantut, and T. Esslinger, Observation of quantized conductance in neutral matter, Nature (London) 517, 64 (2015).
- 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).
- S. Krinner, T. Esslinger, and J.-P. Brantut, Two-terminal transport measurements with cold atoms, J. Phys.: Condens. Matter 29, 343003 (2017).
- 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).
- 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).
- Y.-H. Wan and Q.-F. Sun, Quarter-quantized thermal Hall effect with parity anomaly, Phys. Rev. B 109, 195408 (2024).
- 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).
- 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).
- L. Arrachea, G. S. Lozano, and A. A. Aligia, Thermal transport in one-dimensional spin heterostructures, Phys. Rev. B 80, 014425 (2009).
- 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).
- 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.
- L. Peralta Gavensky, G. Usaj, and C. A. Balseiro, Nonequilibrium edge transport in quantum Hall based Josephson junctions, Phys. Rev. B 103, 024527 (2021).
- Q. Niu, D. J. Thouless, and Y.-S. Wu, Quantized Hall conductance as a topological invariant, Phys. Rev. B 31, 3372 (1985).
- 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).
- 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).
- 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.