# [Seminar] Tensor network approach to Kitaev spin liquid

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### Description

### Speaker

__Prof. Tsuyoshi Okubo / The University of Toyo__

Tsuyoshi Okubo is a project associate professor at Graduate School of Science, University of Tokyo. His research field is in statistical physics, frustrated magnetism, and computational physics. In recent years, he has been interested in tensor network approaches. He received his Ph.D. in Physics from Kyushu University, Japan, in 2008. After he worked as a postdoc under the supervision o Prof. Kawamura at Osaka University until 2012, he moved to Institute for Solid State Physics (ISSP), University of Tokyo, as a project researcher. Since 2017, he has worked in Graduate School of Science, University of Tokyo.

### Title

Tensor network approach to Kitaev spin liquid

### Abstract

The Kitaev model on the honeycomb lattice has been widely investigated as a fundamental model to investigate the nature of the quantum spin liquid in two-dimension [1,2]. In the Kitaev model, the interactions are Ising type, Sγ Sγ, and the spin component γ=x,y,z is determined from the direction to the neighboring site. The ground state is known to be a spin liquid state, in which the nature is described by Majorana fermions [1].

The Kitaev model on the honeycomb lattice has been widely investigated as a fundamental model to investigate the nature of the quantum spin liquid in two-dimension [1,2]. In the Kitaev model, the interactions are Ising type, Sγ Sγ, and the spin component γ=x,y,z is determined from the direction to the neighboring site. The ground state is known to be a spin liquid state, in which the nature is described by Majorana fermions [1]. When we apply a magnetic field to the Kitaev system, the excitation spectrum described by the mobile Majorana fermions opens a gap, and the ground state changes to a topological spin liquid, where a half-integer thermal Hall conductivity emerges in the low-temperature limit [1]. In the recent experiment on α-RuCl3 under a moderate magnetic field, a similar half-integer thermal Hall conductivity was observed at a finite temperature [3], although its ground state seems to be a magnetically ordered state at zero magnetic field due to off-diagonal and (long-range) Heisenberg interactions.

In this talk, we investigate finite temperature properties of the Kitaev model with/without off-diagonal interactions by tensor network approach. We represent a density operator of the system as a network consist of small tensors. In particular, we use the tensor product state (TPO) to approximate the density operator [1]. We show that by this approach, we can qualitatively reproduce a double peak structure in the temperature dependence of the specific heat, while the low-temperature peak height is much smaller than that obtained by quantum Monte Carlo [4]. We also discuss the behaviors of the thermal Hall conductivity at finite temperatures [5].

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

[2] Y. Motome and J. Nasu, J. Phys. Soc. Jpn. 89, 012002 (2020).

[3] Y. Kasahara, T. Ohnishi, Y. Mizukami, et al., Nature, 559, 227 (2018).

[4] J. Nasu, M. Udagawa, and, Y. Motome, Phys. Rev. B 92, 115122 (2015).

[5] T. Okubo, J. Nasu, T. Misawa, and Y. Motome, in preparation.

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981 9709 3580

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