- Editors' Suggestion
- Open Access
Transient localization from fractionalization: Vanishingly small energy transport in gapless quantum magnets
Phys. Rev. B 114, 034423 – Published 21 July, 2026
DOI: https://doi.org/10.1103/crq3-l1r3
Abstract
In this work, we investigate zero-temperature energy transport in a gapless quantum magnet. We find that suppressed energy transport can arise at low frequencies due to transient localization from fractionalization, even in the absence of extrinsic defects or disorder. Concretely, we consider a Kitaev ladder model, whose spin degrees of freedom fractionalize into visons and spinons, in a uniform magnetic field. For moderate magnetic fields, visons are heavy and act as quasistatic disorder that induces transient localization of light spinons even in the translation-invariant model and at zero temperature, which strongly suppresses the residual transport.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (63)
- X.-G. Wen, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, Oxford, 2007).
- S. Sachdev, Quantum Phases of Matter (Cambridge University Press, Cambridge, 2023).
- X.-G. Wen, Quantum orders and symmetric spin liquids, Phys. Rev. B 65, 165113 (2002).
- L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
- C. Broholm, R. Cava, S. Kivelson, D. Nocera, M. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020).
- J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
- L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
- P.-L. Dai, G. Zhang, Y. Xie, C. Duan, Y. Gao, Z. Zhu, E. Feng, Z. Tao, C.-L. Huang, H. Cao, A. Podlesnyak, G. E. Granroth, M. S. Everett, J. C. Neuefeind, D. Voneshen, S. Wang, G. Tan, E. Morosan, X. Wang, H.-Q. Lin, et al., Spinon Fermi surface spin liquid in a triangular lattice antiferromagnet , Phys. Rev. X 11, 021044 (2021).
- S. Yamashita, T. Yamamoto, Y. Nakazawa, M. Tamura, and R. Kato, Gapless spin liquid of an organic triangular compound evidenced by thermodynamic measurements, Nat. Commun. 2, 275 (2011).
- N. Li, M. T. Xie, Q. Huang, Z. W. Zhuo, Z. Zhang, E. S. Choi, Y. Y. Wang, H. Liang, Y. Sun, D. D. Wu, Q. J. Li, H. D. Zhou, G. Chen, X. Zhao, Q. M. Zhang, and X. F. Sun, Thermodynamics and heat transport in the quantum spin liquid candidates and , Phys. Rev. B 110, 224414 (2024).
- Y. Matsuda, T. Shibauchi, and H.-Y. Kee, Kitaev quantum spin liquids, Rev. Mod. Phys. 97, 045003 (2025).
- Y. J. Yu, Y. Xu, K. J. Ran, J. M. Ni, Y. Y. Huang, J. H. Wang, J. S. Wen, and S. Y. Li, Ultralow-temperature thermal conductivity of the Kitaev honeycomb magnet across the field-induced phase transition, Phys. Rev. Lett. 120, 067202 (2018).
- X. Hong, M. Gillig, W. Yao, L. Janssen, V. Kocsis, S. Gass, Y. Li, A. U. B. Wolter, B. Büchner, and C. Hess, Phonon thermal transport shaped by strong spin-phonon scattering in a Kitaev material , npj Quantum Mater. 9, 18 (2024).
- Y. Xu, J. Zhang, Y. S. Li, Y. J. Yu, X. C. Hong, Q. M. Zhang, and S. Y. Li, Absence of magnetic thermal conductivity in the quantum spin-liquid candidate , Phys. Rev. Lett. 117, 267202 (2016).
- Y. Lyu, L. Pritchard Cairns, J. Rodriguez, C. Liu, K. Ng, J. Singleton, and J. G. Analytis, Entanglement randomness and gapped itinerant carriers in a frustrated quantum magnet, Phys. Rev. X 15, 041035 (2025).
- P. Bourgeois-Hope, F. Laliberté, E. Lefrançois, G. Grissonnanche, S. R. de Cotret, R. Gordon, S. Kitou, H. Sawa, H. Cui, R. Kato, L. Taillefer, and N. Doiron-Leyraud, Thermal conductivity of the quantum spin liquid candidate : No evidence of mobile gapless excitations, Phys. Rev. X 9, 041051 (2019).
- J. M. Ni, B. L. Pan, B. Q. Song, Y. Y. Huang, J. Y. Zeng, Y. J. Yu, E. J. Cheng, L. S. Wang, D. Z. Dai, R. Kato, and S. Y. Li, Absence of magnetic thermal conductivity in the quantum spin liquid candidate , Phys. Rev. Lett. 123, 247204 (2019).
- A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321, 2 (2006).
- M. Schiulaz and M. Müller, Ideal quantum glass transitions: Many-body localization without quenched disorder, AIP Conf. Proc. 1610, 11 (2014).
- W. De Roeck and F. Huveneers, Asymptotic quantum many-body localization from thermal disorder, Commun. Math. Phys. 332, 1017 (2014).
- Z. Papić, E. M. Stoudenmire, and D. A. Abanin, Many-body localization in disorder-free systems: The importance of finite-size constraints, Ann. Phys. 362, 714 (2015).
- N. Y. Yao, C. R. Laumann, J. I. Cirac, M. D. Lukin, and J. E. Moore, Quasi-many-body localization in translation-invariant systems, Phys. Rev. Lett. 117, 240601 (2016).
- N. Darkwah Oppong, G. Pasqualetti, O. Bettermann, P. Zechmann, M. Knap, I. Bloch, and S. Fölling, Probing transport and slow relaxation in the mass-imbalanced Fermi-Hubbard model, Phys. Rev. X 12, 031026 (2022).
- 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).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/crq3-l1r3 for details of the effective theory and its calculation, additional results on MPS simulation and its convergence, which includes Refs. [59, 60, 61, 62, 63].
- K. B. Yogendra, T. Das, and G. Baskaran, Emergent glassiness in the disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting, Phys. Rev. B 108, 165118 (2023).
- S. Feng, A. Agarwala, S. Bhattacharjee, and N. Trivedi, Anyon dynamics in field-driven phases of the anisotropic Kitaev model, Phys. Rev. B 108, 035149 (2023).
- K. Wang, S. Feng, P. Zhu, R. Chi, H.-J. Liao, N. Trivedi, and T. Xiang, Fractionalization signatures in the dynamics of quantum spin liquids, Phys. Rev. B 111, L100402 (2025).
- B. Paredes, F. Verstraete, and J. I. Cirac, Exploiting quantum parallelism to simulate quantum random many-body systems, Phys. Rev. Lett. 95, 140501 (2005).
- R. Chitra and T. Giamarchi, Critical properties of gapped spin-chains and ladders in a magnetic field, Phys. Rev. B 55, 5816 (1997).
- T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, 2003).
- E. S. Sørensen, A. Catuneanu, J. S. Gordon, and H.-Y. Kee, Heart of entanglement: Chiral, nematic, and incommensurate phases in the Kitaev-gamma ladder in a field, Phys. Rev. X 11, 011013 (2021).
- T. D. Kühner and S. R. White, Dynamical correlation functions using the density matrix renormalization group, Phys. Rev. B 60, 335 (1999).
- A. Nocera and G. Alvarez, Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors, Phys. Rev. E 94, 053308 (2016).
- J. Nasu, M. Udagawa, and Y. Motome, Thermal fractionalization of quantum spins in a Kitaev model: Temperature-linear specific heat and coherent transport of Majorana fermions, Phys. Rev. B 92, 115122 (2015).
- P. Zhu, S. Feng, K. Wang, T. Xiang, and N. Trivedi, Emergent quantum Majorana metal from a chiral spin liquid, Nat. Commun. 16, 2420 (2025).
- J. Hauschild, J. Unfried, S. Anand, B. Andrews, M. Bintz, U. Borla, S. Divic, M. Drescher, J. Geiger, M. Hefel, K. Hémery, W. Kadow, J. Kemp, N. Kirchner, V. S. Liu, G. Möller, D. Parker, M. Rader, A. Romen, S. Scalet, et al., Tensor network Python (TeNPy) version 1, SciPost Phys. Codebases 41 (2024).
- J. M. Luttinger, Theory of thermal transport coefficients, Phys. Rev. 135, A1505 (1964).
- A. Troisi and G. Orlandi, Charge-transport regime of crystalline organic semiconductors: Diffusion limited by thermal off-diagonal electronic disorder, Phys. Rev. Lett. 96, 086601 (2006).
- J. Keski-Rahkonen, X. Ouyang, S. Yuan, A. M. Graf, A. Aydin, and E. J. Heller, Quantum-acoustical Drude peak shift, Phys. Rev. Lett. 132, 186303 (2024).
- H. Rammal, A. Ralko, S. Ciuchi, and S. Fratini, Transient localization from the interaction with quantum bosons, Phys. Rev. Lett. 132, 266502 (2024).
- A. P. Joy and A. Rosch, Dynamics of visons and thermal Hall effect in perturbed Kitaev models, Phys. Rev. X 12, 041004 (2022).
- H.-K. Jin, J. Knolle, and M. Knap, Fractionalized prethermalization in a driven quantum spin liquid, Phys. Rev. Lett. 130, 226701 (2023).
- A. Smith, J. Knolle, D. L. Kovrizhin, and R. Moessner, Disorder-free localization, Phys. Rev. Lett. 118, 266601 (2017).
- G.-Y. Zhu and M. Heyl, Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium, Phys. Rev. Res. 3, L032069 (2021).
- A. Metavitsiadis and W. Brenig, Flux mobility delocalization in the Kitaev spin ladder, Phys. Rev. B 103, 195102 (2021).
- T. Senthil and M. P. A. Fisher, Quasiparticle localization in superconductors with spin-orbit scattering, Phys. Rev. B 61, 9690 (2000).
- C. R. Laumann, A. W. W. Ludwig, D. A. Huse, and S. Trebst, Disorder-induced Majorana metal in interacting non-Abelian anyon systems, Phys. Rev. B 85, 161301(R) (2012).
- C. N. Self, J. Knolle, S. Iblisdir, and J. K. Pachos, Thermally induced metallic phase in a gapped quantum spin liquid: Monte Carlo study of the Kitaev model with parity projection, Phys. Rev. B 99, 045142 (2019).
- 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).
- V. Dobrosavljević, A. A. Pastor, and B. K. Nikolić, Typical medium theory of Anderson localization: A local order parameter approach to strong-disorder effects, Europhys. Lett. 62, 76 (2003).
- J. Chaloupka and G. Khaliullin, Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates , Phys. Rev. B 92, 024413 (2015).
- Y.-F. Jiang, T. P. Devereaux, and H.-C. Jiang, Field-induced quantum spin liquid in the Kitaev-Heisenberg model and its relation to , Phys. Rev. B 100, 165123 (2019).
- H. Li, X.-G. Zhou, G. Su, and W. Li, Kitaev-derived gapless spin liquid in the quantum magnet , npj Quantum Mater. (2026).
- B. P. Belbase, A. Unnikrishnan, S. Feng, E. S. Choi, J. Knolle, and A. Banerjee, Finite spinon density-of-states in triangular-lattice delafossite , arXiv:2504.05436.
- S. Feng, P. Zhu, J. Knolle, and M. Knap, Zenodo entry for: Transient localization from fractionalization: Vanishingly small energy transport in gapless quantum magnets, Zenodo, 2025, https://doi.org/10.5281/zenodo.17151126.
- 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).
- 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).
- E. Lieb, Flux phase of the half-filled band, Phys. Rev. Lett. 73, 2158 (1994).
- P. Nozières and C. T. De Dominicis, Singularities in the x-ray absorption and emission of metals. III. One-body theory exact solution, Phys. Rev. 178, 1097 (1969).
- S.-S. Zhang, G. B. Halász, and C. D. Batista, Theory of the Kitaev model in a [111] magnetic field, Nat. Commun. 13, 399 (2022).
- M. P. Zaletel, R. S. K. Mong, C. Karrasch, J. E. Moore, and F. Pollmann, Time-evolving a matrix product state with long-ranged interactions, Phys. Rev. B 91, 165112 (2015).