Phase-sensitive quantum-state texture during thermalization of a Dzyaloshinskii-Moriya Heisenberg dimer

Abstract: We investigate quantum-state texture during the thermal relaxation of an anisotropic spin-$1/2$ Heisenberg dimer subject to a longitudinal magnetic field and a Dzyaloshinskii-Moriya (DM) interaction. Starting from local transverse and longitudinal couplings to a bosonic bath, we construct a global weak-coupling Lindblad equation, identify its transition channels, and discuss the applicability and limitations of the secular approximation. The Gibbs state is obtained explicitly in the local spin basis, revealing that the DM coupling controls both the modulus and phase of the single-excitation coherence by modifying the energy splitting and rotating the chiral phase. For heating and cooling protocols, we compare rugosity, fidelity-based texture, and trace-distance texture with coherence, vector spin chirality, and purity. The relaxation dynamics separates population thermalization from the decay and precession of deliberately prepared energy-basis coherence. Their combined contribution to local coherence produces DM-dependent texture overshoots and, during cooling, damped oscillations and sign changes of the coherence quadratures. These transients differ from the evolution of coherence magnitude and purity, while trace-distance texture weights them differently from the overlap-based quantifiers. Calculations at reduced dissipation preserve the texture maxima within the secular model. The results identify a phase-sensitive diagnostic of relaxation.