Thermal State of Kitaev Model with Isometric Tensor Networks

Understanding thermal states and transport properties of quantum spin liquids (QSLs), where heat is carried by emergent quasiparticles from spin fractionalization, is central to the statistical mechanics of strongly correlated phases of matter. The unperturbed Kitaev model on the Honeycomb lattice [1] is paradigmatic, as it is conjectured to host non-Abelian physics, its ground state correlators are exactly solvable with itinerant Majorana fermions and static Z₂ fluxes, and it may provide a description of spin-orbital entangled magnets like α-RuCl₃. Building on prior thermal transport characterizations in [2], we extend the finite-temperature studies of the two-dimensional (2D) Kitaev model using isometric tensor networks (isoTNS) [3] and benchmark thermal Hall conductivities. We further probe thermal response under a magnetic field, where a non-Abelian chiral spin liquid and an intermediate gapless phase are conjectured to exist [5,6]. Our work provides a route to preparing thermal states of QSLs with 2D tensor networks and to characterizing their finite-temperature transport.

[1] A. Kitaev, Ann. Phys. (N. Y.) 321, 2 (2006).

[2] J. Nasu, J. Yoshitake, and Y. Motome, Phys. Rev. Lett. 119, 127204 (2021).

[3] W. Kadow, F. Pollmann, and M. Knap. Phys. Rev. B 107, 205106 (2023).

[4] S.-S. Zhang, G. B. Halász, and C. D. Batista, Nat. Comm. 13, 399 (2022).

[5] P. Zhu, S. Feng, K. Wang, T. Xiang, and N. Trivedi, Nat. Comm. 16, 2420 (2025).