  A central issue of Mott physics, with symmetries being fully retained in the
spin background, concerns the charge excitation. In a two-leg spin ladder with
spin gap, an injected hole can exhibit either a Bloch wave or a density wave by
tuning the ladder anisotropy through a `quantum critical point' (QCP). The
nature of such a QCP has been a subject of recent studies by density matrix
renormalization group (DMRG). In this paper, we reexamine the ground state of
the one doped hole, and show that a two-component structure is present in the
density wave regime in contrast to the single component in the Bloch wave
regime. In the former, the density wave itself is still contributed by a
standing-wave-like component characterized by a quasiparticle spectral weight
$Z$ in a finite-size system. But there is an additional charge incoherent
component emerging, which intrinsically breaks the translational symmetry
associated with the density wave. The partial momentum is carried away by
neutral spin excitations. Such an incoherent part does not manifest in the
single-particle spectral function, directly probed by the angle-resolved
photoemission spectroscopy (ARPES) measurement, however it is demonstrated in
the momentum distribution function. The Landau's one-to-one correspondence
hypothesis for a Fermi liquid breaks down here. The microscopic origin of this
density wave state as an intrinsic manifestation of the doped Mott physics will
be also discussed.
