We generalize the area-law violating models of Fredkin spin chain into two
    dimensions by building a quantum bicolor six-vertex model with correlated
    swapping and alternating boundary condition. The construction is a analogous to
    our first example of such models based on quantum lozenge tiling
    (arXiv:2210.01098), but on a square lattice. The Hamiltonian is frustration
    free, and its projectors generate ergodic dynamics within the subspace of
    height configuration that are non negative. The ground state is a volume- and
    color-weighted superposition of classical bicolor six-vertex configurations
    with non-negative heights in the bulk an zero height on the boundary. The
    entanglement entropy between subsystems has a phase transition as the weight
    parameter is tuned, which is shown to be robust in the presence of an external
    field acting on the color degree of freedom. The ground state transitions
    between area- and volume-law entanglement phases with a critical point where
    entanglement entropy scales as a function $L\log L$ of the linear system size
    $L$. Intermediate scalings between $L\log L$ and $L^2$ can be achieved with an
    inhomogeneous deformation parameter that approaches 1 at different rates in the
    thermodynamic limit.

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