Speaker

Dr. Kiyu Fukui / Department of Applied Physics, The University of Tokyo

Title

Feasibility study of the Kitaev spin liquid and exploration of novel quantum phenomena of the Majorana fermions

Abstract

The Kitaev model provides us with a rare example of exact quantum spin liquid states in more than one dimension [1]. Since the proposal by Jackeli and Khaliullin [2], its abundant candidate materials have been explored intensively [3]. These facts make the Kitaev spin liquid an excellent playground for investigating the physics of quantum spin liquids, especially the intriguing quantum phenomena brought about by the Majorana fermions reflecting the fractionalization of the spins. In the seminar, we will highlight our recent efforts in the following topics in two different directions.

The first direction is the feasibility study of the quantum spin liquid in the extension of the Kitaev model. Thus far, almost all candidates exhibit magnetic ordering at low temperatures and do not achieve a quantum spin liquid state as a ground state due to non-Kitaev interactions, which are inevitably present in the materials. While it is very important to clarify the effect of these additional interactions and to explore new platforms for realizing the Kitaev spin liquid theoretically, extensions of the model make it no longer solvable, and numerical calculations are challenging. Here, we address the feasibility of the quantum spin liquids for three extensions of the model: higher spin materials [4], three-dimensional lattices [5], and ultracold polar molecules [6], by using the pseudofermion functional renormalization group method [7].

The second direction is the exploration of the unprecedented quantum phenomena brought about by the Majorana fermions in the Kitaev spin liquid. As a source of intriguing phenomena, we consider the coupling of the Kitaev model with the environment. One of the efficient methods to study such systems is an effective non-Hermitian Hamiltonian, which incorporates the effects of dissipation. We investigate the effective non-Hermitian Kitaev model [8] under the magnetic field based on the perturbation theory [9]. As another case, we study topological Majorana flat bands in quantum spin liquids by considering the Kitaev model on a periodically depleted honeycomb lattice [10]. In both cases, the novel physics of the Majorana fermions, reflecting the fractionalization of the spins, is revealed.

[1] A. Kitaev, Ann. Phys. 321, 2 (2006).
[2] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).
[3] Y. Motome, R. Sano, S. Jang, Y. Sugita, and Y. Kato, J. Phys.: Condens. Matter 32, 404001 (2020).
[4] K. Fukui, Y. Kato, J. Nasu, and Y. Motome, Phys. Rev. B 106, 174416 (2022).
[5] K. Fukui, Y. Kato, and Y. Motome, J. Phys. Soc. Jpn. 92, 064708 (2023).
[6] K. Fukui, Y. Kato, J. Nasu, and Y. Motome, Phys. Rev. B 106, 014419 (2022).
[7] J. Reuther and P. Wölfle, Phys. Rev. B 81, 144410 (2010).
[8] K. Yang, S. C. Morampudi, and E. J. Bergholtz, Phys. Rev. Lett. 126, 077201 (2021).
[9] K. Fukui, Y. Kato, and Y. Motome, Phys. Rev. B 110, 024429 (2024).
[10] K. Fukui and Y. Motome, in preparation.

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