Coherence dynamics of spin systems in critical environment with topological characterization

The coherence dynamics of the central systems are investigated in the spin-chain environment with topological characterization. For the single- and two-spin coherence, their critical behaviors can detect the topological quantum phase transitions (TQPTs) in weaker coupling regions. Their noncritical behaviors show periodic oscillations or keep constant. For the quantum coherence of a symmetric W state, the bipartite coherence is dominant due to its polygamy. The critical behaviors of global coherence ( \(\textrm{QC}_{\mathrm{a:bc}}\) ${\text{QC}}_{\mathrm{a}:\mathrm{bc}}$ and \(\textrm{QC}_{\mathrm{b:c}}\) ${\text{QC}}_{\mathrm{b}:\mathrm{c}}$ ) and multipartite monogamy can also detect the TQPTs. In the strong coupling regions ( \(g_{a(b,c)} \gg 1\) $g_{a(b,c)}\gg 1$ ), the coherence dynamics of single-spin, two-spin, and bipartite block of three-spin system can be characterized by Gaussian envelope, but the envelope line of three-spin coherence can be only described by negative logarithmic function. Finally, the resistance to the topological spin-chain environment becomes stronger from the single- to three-spin coherence.