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One-dimensional gapped phases that avoid any symmetry breaking have drawnenduring attention. In this paper, we study such phases in a bond-alternatingspin-1 $K$-$\Gamma$ chain built of a Kitaev ($K$) interaction and anoff-diagonal $\Gamma$ term. In the case of isotropic bond strength, a Haldanephase, which resembles the ground state of a spin-$1$ Heisenberg chain, isidentified in a wide region. A gapped Kitaev phase situated at dominantferromagnetic and antiferromagnetic Kitaev limits is also found. The Kitaevphase has extremely short-range spin correlations and is characterized byfinite $\mathbb{Z}_2$-valued quantities on bonds. Its lowest entanglementspectrum is unique, in contrast to the Haldane phase whose entanglementspectrum is doubly degenerate. In addition, the Kitaev phase shows adouble-peak structure in the specific heat at two different temperatures. Inthe pure Kitaev limit, the two peaks are representative of the development ofshort-range spin correlation at $T_h \simeq 0.5680$ and the freezing of$\mathbb{Z}_2$ quantities at $T_l \simeq 0.0562$, respectively. By consideringbond anisotropy, regions of Haldane phase and Kitaev phase are enlarged,accompanied by the emergence of dimerized phases and three distinctmagnetically ordered states.

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