  We study one-flavor $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ lattice QCD in
($1+1$) dimensions at zero temperature and finite density using matrix product
states and the density matrix renormalization group. We compute physical
observables such as the equation of state, chiral condensate, and quark
distribution function as functions of the baryon number density. As a physical
implication, we discuss the inhomogeneous phase at nonzero baryon density,
where the chiral condensate is inhomogeneous, and baryons form a crystal. We
also discuss how the dynamical degrees of freedom change from hadrons to quarks
through the formation of quark Fermi seas.
