Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice

We study the thermodynamic behavior of modified spin-S Kitaev models introduced by Baskaran, Sen, and Shankar [Phys. Rev. B 78, 115116 (2008)]. These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high-temperature expansions, and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin S = 1 and S = 2. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as T -> 0, become critical as T -> 0, or diverge exponentially as T -> 0. The Z(2) flux variable associated with each hexagonal plaquette saturates at the value +1 as T -> 0 in all models except the S = 1 antiferromagnet where the mean flux remains zero as T -> 0. We provide qualitative explanations for these results.

Automated summary

This study examines the thermodynamic behavior of modified spin-S Kitaev models, finding distinct properties for half-odd-integer spins and integer spins. Various thermodynamic properties are explored through transfer matrix methods, high-temperature expansions, and Monte Carlo simulations for ferromagnetic and antiferromagnetic models with spin S = 1 and S = 2. The results reveal a range of behaviors, including finite, critical, or exponential correlation lengths as temperature approaches zero, as well as differences in the saturation of Z(2) flux variables among different models.