Fig. 6.

Underlying phase diagram. Underlying phase diagram with Γ′ = 0 and θ = 0 in the Γ/K − h plane as calculated with DRMG for N = 200 and OBC. Spin–spin correlations a $⟨S_j^x{S}_k^x⟩$ and b $⟨S_j^z{S}_k^z⟩$ at k − j = 50 are absent within the KΓSL and the KSL phases at h = 0, and develop under the field. Phase boundaries, determined by smoothed fits to the peaks of of χ_h and χ_Γ/K, are drawn as red lines, and separate the KΓSL and the PS from the intervening KSL. c Plaquette expectation 〈W_p〉 differentiates the KΓSL and the KSL as it changes sign across the transition. d Plaquette–plaquette correlations $⟨W_p{W}_{p\prime }⟩$ at p′ − p = 30 are small in the PS and become appreciable within the KΓSL and KSL, approaching ${⟨W_p⟩}^2$ in the limit of large separation