Ground State of the Spin-1/2 Honeycomb Γ Model: Zigzag Magnetic Order

The off-diagonal symmetric interaction, Γ ( S_i^α S^β_i+γ + S_i^β S^α_i+γ ), has sprung to prominence
as a competing term in the spin Hamiltonians of candidate Kitaev materials. We investigate
the quantum (S = 1/2) Γ model on the honeycomb lattice using the tensor-network method of
infinite projected entangled pair states (iPEPS). We demonstrate that the ground state is a
zigzag magnetically ordered state, rather than the spin liquid reported on the basis of density-matrix
renormalization-group (DMRG) studies. By applying two quasi-one-dimensional numerical
treatments, the infinite matrix-product-state (iMPS) and DMRG methods, we show that
this contrast is a consequence of the system size considered. Thus the quantum Γ model
is quite different from its classical counterpart, which is a classical spin liquid due to its
macroscopic ground-state degeneracy.