Tensor-Network-Based Approach to Kitaev Spin Liquid

Tsuyoshi Okubo^1*

¹Institute for Physics of Intelligence, University of Tokyo, Tokyo, Japan

* Presenter:Tsuyoshi Okubo, email:t-okubo@phys.s.u-tokyo.ac.jp

To represent a quantum many-body state, we need to treat huge vectors in exponentially increasing dimensions as we increase the number of particles. Such an exponentially large vector space is a fundamental difficulty in treating quantum many-body problems in classical computers. The tensor network representations can express a quantum many-body state efficiently, and we can accurately calculate physical quantities with polynomial costs. Although tensor network methods are so powerful, there remain difficulties in investigating quantum spin liquids that contain larger quantum entanglement.
In this talk, we investigate the honeycomb lattice Kitaev model with/without off-diagonal interactions by tensor network approach. The ground state of the Kitaev model is a spin liquid state, in which the nature is characterized by Majorana fermions. When we apply a magnetic field to the Kitaev system, the excitation spectrum represented by the mobile Majorana fermions opens its gap, and the ground state changes to a topological spin liquid, where a half-integer thermal Hall conductivity emerges in the low-temperature limit.
To investigate the finite temperature properties of the model, we use the infinite tensor product state (iTPO) to approximate the density operator. We show that by this approach, we can qualitatively reproduce a double peak structure in the temperature dependence of the specific heat. In contrast, the low-temperature peak height is much smaller than that obtained by quantum Monte Carlo. We will discuss how the accuracy in the low-temperature region can be improved when we consider an optimization scheme based on hexagonal clusters.
We also discuss the possibility of using tensor network representations to design an efficient quantum circuit suitable for near-future noisy quantum computers. For the Kitaev model, a simple tensor network state can capture the qualitative properties of the spin liquid. By adding short-range excitations, we can also systematically improve its energy expectation value. We will show that a similar procedure can be applied to the variational quantum eigensolver (VQE) approach by representing tensor network states as quantum circuits. We will discuss that we can efficiently optimize the infinite system by solving an optimization problem in small clusters through this approach.

Keywords: Tensor network, Kitaev model, Spin liquid, Quantum computing