Temperature evolution of the spin correlation and excitation spectrum is investigated for the Kitaev model defined on a decorated honeycomb lattice by using the quantum Monte Carlo simulation in the Majorana fermion representation. The ground state of this quantum spin model is given by two kinds of chiral spin liquids: one is topologically trivial with Abelian anyon excitations, and the other is topologically nontrivial with non-Abelian anyon excitations. While lowering temperature, the model exhibits several crossovers in the paramagnetic state, which originate from the fractionalization of quantum spins into Majorana fermions, in addition to a phase transition associated with time reversal symmetry breaking. We show that the spin correlation develops around the crossover temperatures, whereas it shows a slight change at the critical temperature, as in other Kitaev-type models. We also calculate the excitation spectrum in terms of Majorana fermions, and find that the excitation gap in the non-Abelian phase is fragile against thermal fluctuations of the Z 2 fluxes, while that in the Abelian phase remains open.
Temperature evolution of the spin correlation and excitation spectrum is investigated for a Kitaev model defined on a decorated honeycomb lattice by using the quantum Monte Carlo simulation in the Majorana fermion representation. The ground state of this quantum spin model is given by two kinds of chiral spin liquids: one is topologically trivial with Abelian anyon excitations, and the other is topologically nontrivial with non-Abelian anyon excitations. While lowering temperature, the model exhibits several crossovers in the paramagnetic state, which originate from the fractionalization of quantum spins into Majorana fermions, in addition to a phase transition associated with time reversal symmetry breaking. We show that the spin correlation develops around the crossover temperatures, whereas it shows a slight change at the critical temperature, as in other Kitaev-type models. We also calculate the excitation spectrum in terms of Majorana fermions, and find that the excitation gap in the non-Abelian phase is fragile against thermal fluctuations of the
Z2 fluxes, while that in the Abelian phase remains open.
Thermodynamic properties of chiral spin liquids are investigated for a variant of the Kitaev model defined on a decorated honeycomb lattice. Using the quantum Monte Carlo simulation, we find that the model exhibits a finite-temperature phase transition associated with the time reversal symmetry breaking, in both topologically trivial and nontrivial regions. Numerical results for the Chern number and the thermal Hall conductivity indicate that the phase transition changes from a continuous to a discontinuous transition as we vary the coupling constants to reach the non-Abelian phase coming from the Abelian phase of the model. In addition, we find as a diagnostic of the chiral spin liquids, successive crossovers with multistage entropy release above the critical temperature, which indicates that the hierarchical fractionalization of a quantum spin occurs differently between the two regions.
A three-dimensional Kitaev model on a hyperhoneycomb lattice is investigated numerically at finite temperature. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with Z 2 variables. The density of states of Majorana fermions shows an excitation gap in the gapped region, while it is semimetallic in the gapless region reflecting the Dirac node. Performing the Monte Carlo simulation, we calculate the temperature dependence of the Majorana spectra. We find that the semimetallic dip is filled as temperature increases in the gapless region, but surprisingly, the spectrum develops an excitation gap in the region near the gapless-gapped boundary. Such changes of the low-energy spectrum appear sharply at the transition temperature from the spin liquid to the paramagnetic state. The results indicate that thermal fluctuations of the Z 2 fields significantly influence the low-energy state of Majorana fermions, especially in the spin liquid formation.
An effective model in the isolated dimer limit of the Kitaev-type model on a decorated honeycomb lattice is investigated at finite temperature. The ground state of this model is exactly shown to be a chiral spin liquid with spontaneous breaking of time reversal symmetry. We elab- orate the finite-temperature phase diagram by using the mean-field approximation and Monte Carlo simulation. We find that the phase transition between the high-temperature paramagnetic phase and the low-temperature chiral spin liquid phase is always of second order in the Monte Carlo results, although a tricritical point appears in the mean-field phase diagram. The finite-size scaling analysis of the Monte Carlo data suggests that the phase transition belongs to the two-dimensional Ising universality class.
Finite-temperature (
T) properties of a Kitaev model defined on a honeycomb lattice are investigated by a quantum Monte Carlo simulation, from the viewpoint of fractionalization of quantum
S=1/2 spins into two types of Majorana fermions, itinerant and localized. In this system, the entropy is released successively at two well-separated
T scales, as a clear indication of the thermal fractionalization. We show that the high-
T crossover, which is driven by itinerant Majorana fermions, is closely related with the development of nearest-neighbor spin correlations. On the other hand, the low-
T crossover originates in thermal fluctuations of fluxes composed of localized Majorana fermions, by which the spectrum of itinerant Majorana fermions is significantly disturbed. As a consequence, in the intermediate-
T range, the system exhibits coherent transport of Majorana fermions and
T-linear behavior in the specific heat, despite the Dirac semimetallic spectrum in the low-
T limit. We also show that the flux fluctuations affect the gapless-gapped phase boundary. Our results indicate that the fractionalization is experimentally observable in spin correlations, specific heat, and transport properties.
The Kitaev model, defined on a honeycomb lattice, features an exactly solvable ground state with fractionalized Majorana fermion excitations, which can potentially form non-Abelian anyons crucial for fault-tolerant topological quantum computing. Although Majorana fermions are essential for obtaining the exact ground state, their physical interpretation in terms of spin operators remains unclear. In this study, we employ a Green's function approach that maintains SU(2) symmetry to address this issue and explore the model's finite temperature properties. Our results demonstrate that the computed temperature dependence of the correlation functions closely approximates the exact values at zero temperature, confirming the accuracy of our method. We also present several exact results concerning the spin Green's function and spin-spin correlation functions that are specific to the Kitaev model.