Since boundaries play a role of impurity, the Fermi sea disturbed by the boundary generates the 2 k_F oscillation which is observed in various quantities, where k_F is the Fermi wavevector. In the density matrix renormalization group method, which is a powerful numerical method for one-dimensional strongly-correlated systems, the 2 k_F oscillation due to the open boundary condition causes a numerical difficulty. To avoid the difficulty, several smooth boundary conditions have been studied. Recently, the sinusoidal square deformation (SSD) was proposed. Surprisingly, the SSD works well not only numerically but also exactly in some cases. That is, the many body wave function under the periodic boundary condition is exactly equal to that under the open boundary condition with the SSD. The reason is clearly understood by the Fermi sea. Extending the SSD toward more general cases, we propose a real-time manipulation to decouple quantum systems without disturbing the Fermi sea. This decoupling operation opens a way to real-time spatial separation of the gapless Fermi liquid system without losing quantum entanglement.
 A. Gendiar, et.al., Prog. Theor. Phys. 122, 953 (2009); ibid, Phys. 123, 393 (2010).<p>
 IM, et.al., Phys. Rev. B 84, 165132 (2011).