Tensor network wave function of S=1 Kitaev spin liquids

Abstract

The spin-1/2 Kitaev model offers the exactly solvable example of quantum spin liquids. Possible material realizations of the spin-1/2 Kitaev systems and the prospect of using the Majorana fermion excitations for quantum computations have revolutionized quantum spin liquids research. Recently it has been suggested that higher-spin, especially spin-1, Kitaev exchange interactions can be realized in a variety of materials. Numerical computations on small clusters indicate that the ground state of the spin-1 Kitaev model may also be a quantum spin liquid. On the other hand, the nature of the ground state remains elusive since the spin-1 model is not exactly solvable in contrast to the spin-1/2 model. In this work, using the quantum-entanglement based tensor network approach, we construct an explicit ground-state wave function for the spin-1 Kitaev model, which is written only in terms of physical spin operators. We establish the existence of distinct topological sectors on a torus by constructing the minimally entangled states in the degenerate ground-state manifold and evaluating topological entanglement entropy. Our results suggest that the ground state of the spin-1 Kitaev model is a gapped quantum spin liquid with Z 2 gauge structure and Abelian quasiparticles. We explain the subtle differences between the spin-1/2 and spin-1 Kitaev quantum spin liquids.

Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$Γ$ chain

“…We find that the ground-state energy of the isotropic Kitaev chain is -0.603560592(3) 1 , which matches perfectly with a previous estimate by exact diagonalization method [33]. Also of interest is that the energy is very close to that of the two-dimensional spin-1 Kitaev honeycomb model [51]. To capture the QPT driven by Γ interaction, we define the averaged bond density…”

Majorana correlations in the Kitaev model with ordered-flux structures

“…We have discussed the effect of the randomness in the flux configuration to clarify that power law behavior appears in the Majorana correlations. It is also interesting to discuss how robust Majorana correlations are in the related models such as the bilayer Kitaev model [39][40][41], Kitaev-Heisenberg model [10], and higher spin models [42][43][44][45][46][47][48].…”

Excitation spectrum of spin-1 Kitaev spin liquids

“…Recently, microscopic mechanism to realize a S = 1 Kitaev model and candidate materials have been proposed [15], raising the importance of the study of the higher-spin Kitaev physics. Different from its spin-1/2 counterpart, the higher-spin Kitaev model cannot be exactly solved by mapping the spins to Majorana fermions, and numerical studies have been carried out to identify the nature of the ground states for the S = 1 Kitaev model [16][17][18][19][20][21]. While several studies suggest that the isotropic spin-1 Kiatev model exhibits spin liquids with a Z 2 gauge structure, quantitative features about the fractionalized excitations, i.e., the excitations spectrum, are still missing.…”

“…In this letter, we compute the excitation spectrum for the isotropic spin-1 Kitaev model, exploiting the correspondence between the TM spectrum and low-energy excitations developed in the TN formalism. We construct the Z 2 -invariant PEPS [25,31] to represent the spin-1 Kitaev model's ground state by applying a loop gas (LG) projector [20,32] on the state generated by imaginary time evolution (ITE) [33]. We identify the nature of Z 2 QSL of the spin-1 Kitaev model by evaluating the virtual order parameters naturally defined in Z 2 -invariant PEPS [28].…”

“…= 0 broken a single Z 2 vortex w p = −1 at the starting point of the halfinfinite Z string [20]. Similarly, the single X creating charge anyon on site i correspond to a physical half-infinite string operator…”