  Studying the relations between entanglement and coherence is essential in
many quantum information applications. For this, we consider the concurrence,
intrinsic concurrence and first-order coherence, and evaluate the proposed
trade-off relations between them. In particular, we study the temporal
evolution of a general two-qubit XYZ Heisenberg model with asymmetric
spin-orbit interaction under decoherence and analyze the trade-off relations of
quantum resource theory. For XYZ Heisenberg model, we confirm that the
trade-off relation between intrinsic concurrence and first-order coherence
holds. Furthermore, we show that the lower bound of intrinsic concurrence is
universally valid, but the upper bound is generally not. These relations in
Heisenberg models can provide a way to explore how quantum resources are
distributed in spins, which may inspire future applications in quantum
information processing.
