Given an initial state written, in the full Hilber Space, as

$$

|\psi\rangle = \otimes_{j=1}^{L/2}|\leftarrow\rangle \otimes_{j=L/2+1}^L |\rightarrow\rangle,

$$

such that,

$$

\hat{\sigma}_x |\leftarrow\rangle = +|\leftarrow\rangle\

$$

$$

\hat{\sigma}_x |\rightarrow\rangle = -|\rightarrow\rangle.

$$

How can I write it in the form of an MPS?