Ground-state and thermodynamic properties of an $S=1$ Kitaev model

TL;DR

This paper investigates the ground-state and finite-temperature properties of an $S=1$ Kitaev model, revealing a gapless ground state and providing large-scale numerical analysis of its thermodynamic behavior.

Contribution

It is the first comprehensive study of the $S=1$ Kitaev model's ground state and thermodynamics, highlighting the gapless nature and symmetry properties.

Findings

Ground state is a singlet with energy ~ -0.65J per site.

Lowest excited state is in the same subspace as the ground state.

The energy gap decreases with increasing system size, indicating gapless behavior.

Abstract

We study ground-state and thermodynamic properties of an $S=1$ Kitaev model. We first clarify the existence of global parity symmetry in addition to the local symmetry on each plaquette, which enables us to perform the large scale calculations up to 24 sites. It is found that the ground state should be singlet and its energy is estimated as $E/N\sim -0.65J$, where $J$ is the Kitaev exchange coupling. We find that a lowest excited state belongs to the same subspace as the ground state and the gap monotonically decreases with increasing system size, which suggests that the ground state of the $S=1$ Kitaev model is gapless. By means of the thermal pure quantum states, we clarify finite temperature properties characteristic of the Kitaev models with $S\le 2$.