Unveiling the phase diagram of a bond-alternating spin-1/2 K-Γ chain

The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev (K) interaction and a symmetric off-diagonal Gamma interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-1/2 g(x)-g(y) K-Gamma chain by density-matrix renormalization-group method where g(x) and g(y) are the bond strengths of the odd and even bonds, respectively. The phase diagram is dominated by even-Haldane (g(x) > g(y)) and odd-Haldane (g(x) < g(y)) phases where the former is topologically trivial while the latter is a symmetry-protected topological phase. Near the antiferromagnetic Kitaev limit, there are two gapped A(x) and A(y) phases characterized by distinct nonlocal string correlators. In contrast, the isotropic ferromagnetic (FM) Kitaev point serves as a multicritical point where two topological phase transitions meet. The remaining part of the phase diagram contains three symmetry-breaking magnetic phases. One is a sixfold degenerate FMU6 phase where all the spins are parallel to one of the +/-<(x)over cap>, +/-(y) over cap, and +/-(z) over cap axes in a six-site spin-rotated basis, while the other two have more complex spin structures with all the three spin components being finite. Existence of a rank-two spin-nematic ordering in the latter is also discussed.