We investigate the phase diagram of a quantum mixed-spin $(1/2,1/2,1,1)$ Heisenberg tetramer chain featuring bond-alternating antiferromagnetic nearest-neighbor exchange interactions and single-ion anisotropy. This model exhibits a rich phase structure comprising three gapped phases: the antiferromagnetic, topological valence-bond-solid (TVBS), and the trivial nonmagnetic phases (TnM). We identify a multicritical Wess-Zumino-Witten $SU{\left(2\right)}_1$ point where two Ising critical lines merge, forming a higher-symmetry point that realizes conformal embedding on the lattice. Beyond this multicritical point, a Gaussian critical line emerges, determining the boundary between the TVBS and the TnM phases. Utilizing the tangential finite-size scaling method, we demonstrate the precision with which critical points and correlation length critical exponents can be extracted along this Gaussian line. Our results reveal rich critical phenomena induced by the interplay of bond-alternating exchange and anisotropic single-ion interactions in quantum many-body systems.

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• Density matrix renormalization group
• Quantum entanglement
• Symmetry protected topological states
• 1-dimensional spin chains
• Finite-size scaling