  We revisit unitary representation of centrally extended (2 | 2) excitation
superalgebra. We find most generally that `pseudo-momentum', not lattice
momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic
spin chain. All known results point to lattice momentum diagonalization for N=4
super Yang-Mills theory. Having different interacting structure, we ask if N=6
superconformal Chern-Simons theory provides an example of pseudo-momentum
diagonalization. For SO(6) sector, we study maximal shuffling and
next-to-maximal shuffling terms in the dilatation operator and compare them
with results expected from psu(2|2) superalgebbra and integrability. At two
loops, we rederive maximal shuffling term (3-site) and find perfect agreement
with known results. At four loops, we first find absence of next-to-maximal
shuffling term (4-site), in agreement with prediction based on integrability.
We next extract maximal shuffling term (5-site), the most relevant term for
checking the possibility of pseudo-momentum diagonalization. Curiously, we find
that result agrees with integraility prediction based on lattice momentum, as
in N=4 super Yang-Mills theory. Consistency of our results is fully ensured by
checks of renormalizability up to six loops.
