Leon Balents and Matthew P. A. Fisher claimed the following without any further explanation ($N$ is the number of chains)
For a system of $N$ coupled 1D chains, the number of gapless charge modes can vary from $0$ to $N$, and likewise for spin.
in the introduction part of their highly-cited article Weak-coupling phase diagram of the two-chain Hubbard model,
Phys. Rev. B 53, 12133 (1996).
This article studied two Hubbard chains (1D) coupled by simplest single-particle hopping between chains without altering site/spin index. The possible phases therein can be characterized by the number of gapless charge and spin modes. The form of coupling doesn't look to be the reason. From the context, it sounds valid in general.
Can anyone shed some light on this very general conclusion?