Anisotropy as a diagnostic test for distinct tensor network wavefunctions of integer and half-integer spin Kitaev quantum spin liquids

Abstract

Contrasting ground states of quantum magnets with the integer and half-integer spin moments are the manifestation of many-body quantum interference effects. In this work, we investigate the distinct nature of the integer and half-integer spin quantum spin liquids in the framework of the Kitaevs model on the honeycomb lattice. The models with arbitrary spin quantum numbers are not exactly solvable in contrast to the well-known quantum spin liquid solution of the spin-1/2 system. We use the tensor network wavefunctions for the integer and half-integer spin quantum spin liquid states to unveil the important difference between these states. We find that the distinct sign structures of the tensor network wavefunction for the integer and half-integer spin quantum spin liquids are responsible for completely different ground states in the spatially anisotropic limit. Hence the spatial anisotropy would be a useful diagnostic test for distinguishing these quantum spin liquid states, both in the numerical computations and experiments on real materials. We support this discovery via extensive numerics including the tensor network, DMRG, and exact diagonalization computations.

Excitation spectrum of spin-1 Kitaev spin liquids

“…Interestingly, this is consistent with the argument put forth in Ref. [12] that the integer-spin Kitaev model has bosonic exciations instead of Majorana fermions, indicating that the different sign structures of the integer and halfinteger spin LG projectors may faithfully describe the distinct nature of the integer and half-integer spin Kitaev models [21].…”

“…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]. Due to the fundamental distinction between the integer and half-integer LG projector [21], we found that in contrast to the dispersive Majorana excitation in S = 1/2, the spin-1 Kitaev model possesses a dispersive charge anyon excitation. Also, the TM spectrum suggests the existence of the charge excitations with a small gap at the Γ,K and K points in the Brillouin zone.…”

“…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.…”

“…The Hilbert space is thus divided into sectors according to the eigenvalues of the flux operator w p = ±1. For the spin-1 Kitaev model, it has been numerically shown that the ground state lives in the vortex-free sector w p = +1, ∀p [21,32]. Therefore, the states with w p = −1 for a plaquette p can be understood as a Z 2 vortex quasiparticle.…”

“…where U γ = e iπS γ is the π-rotation operator for a given spin [Fig. 1(b)] [21]. Q LG is a projector to the vortex-free space: [34].…”