<p>In this work, we present an innovative linear relaxation explicit-invariant energy quadratization (EIEQ) scheme, which is specially designed to solve Allen-Cahn (AC) and Cahn-Hilliard (CH) type models. This strategy can be simply called LR-EIEQ scheme. By introducing a quadratic auxiliary variable, the original model is transformed into an equivalent formulation. Furthermore, by harnessing the “zero energy contribution” (ZEC) property, we introduce a non-local auxiliary variable specifically designed to tackle the nonlinear coupling variables. The newly devised method distinguishes itself from traditional invariant energy quadratization (IEQ) or scalar auxiliary variable (SAV) approaches in that it eliminates the need to refactor nonlinear functions into the product of two quadratic functions. Rather, it facilitates a more straightforward reconstruction of the nonlinear terms. Next, we develop distinct numerical algorithms for both models, employing the second-order backward differentiation formula (BDF-2) and Crank-Nicolson (CN) formula. We meticulously prove the energy stability and unique solvability of the proposed schemes, and clearly demonstrate the decoupling of the numerical solution. Through a sophisticated splitting technique, the non-local auxiliary variable effectively decouples all variables within the equivalent model, resulting in multiple linear systems. During each iteration of the time-stepping process, only a minimal number of these linear systems need to be solved, thereby achieving complete decoupling of the variables and markedly boosting computational efficiency. Subsequent numerical simulation tests further validate the stability and reliability of the developed algorithms.</p>