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arXiv:1506.05678 · Physics Procedia

Phase Diagram of the Kitaev-type Model on a Decorated Honeycomb Lattice in the Isolated Dimer Limit

Joji Nasu, Yukitoshi Motome

Published Jan 1, 2015• 1 citation
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Abstract

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.

DOI
10.1016/j.phpro.2015.12.098

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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.
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 Z2Z_2Z2​ 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.
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The quantum spin liquid is an enigmatic entity that is often hard to characterize within the conventional framework of condensed matter physics. We here present theoretical and numerical evidence for the characterization of a quantum spin liquid phase extending from the exact ground state to a finite critical temperature. We investigate a three-dimensional variant of the Kitaev model on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables on a diamond lattice. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from the quantum spin liquid to a paramagnet at a finite critical temperature Tc{T}_{c}Tc​, accompanied by a divergent singularity of the specific heat. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above Tc{T}_{c}Tc​, while it obeys the Curie law at high temperature and approaches a nonzero Van Vleck--type constant at low temperature. Although the susceptibility changes continuously at Tc{T}_{c}Tc​, its temperature derivative shows a critical divergence at Tc{T}_{c}Tc​. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables or of the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition can be interpreted as one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. The correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently discovered hyperhoneycomb compound $\ensuremath{\beta}$-Li2{\text{Li}}_{2}Li2​IrO3{\text{IrO}}_{3}IrO3​ is mentioned.
Higher-order topological insulators are distinguished by the existence of topologically protected modes with codimension two or higher. Here, we report the manifestation of a second-order topological insulator in a two dimensional frustrated quantum magnet, which exhibits topological corner modes. Our exactly solvable model is a generalization of the Kitaev honeycomb model to the Shastry-Sutherland lattice that, besides a chiral spin liquid phase, exhibits a gapped spin liquid with Majorana corner modes, which are protected by two mirror symmetries. This second-order Kitaev spin liquid remains stable in the presence of thermal fluctuations and undergoes a finite-temperature phase transition evidenced in large-scale quantum Monte Carlo simulations.