  The magnetic and thermodynamic properties of spin-1/2 Heisenberg diamond
chains are investigated in three different cases: (a) J1, J2, J3>0
(frustrated); (b) J1, J3<0, J2>0 (frustrated); and (c) J1, J2>0, J3<0
(non-frustrated). The density matrix renormalization group (DMRG) technique is
invoked to study the properties of the system in the ground state, while the
transfer matrix renormalization group (TMRG) technique is applied to explore
the thermodynamic properties. The local magnetic moments, spin correlation
functions, and static structure factors are discussed in the ground state for
the three cases. It is shown that the static structure factor S(q) shows peaks
at wavevectors $q=a\pi /3$ (a=0,1,2,3,4,5) for different couplings in a zero
magnetic field, which, however in the magnetic fields where the magnetization
plateau with m=1/6 pertains, exhibits the peaks only at q=0, $2\pi /3$ and
$4\pi /3$, which are found to be couplings-independent. The DMRG results of the
zero-field static structure factor can be nicely fitted by a linear
superposition of six modes, where two fitting equations are proposed. It is
observed that the six modes are closely related to the low-lying excitations of
the system. At finite temperatures, the double-peak structures of the
susceptibility and specific heat against temperature are obtained, where the
peak positions and heights are found to depend on the competition of the
couplings. It is also uncovered that the XXZ anisotropy of F and AF couplings
leads the system of case (c) to display quite different behaviors. In addition,
the experimental data of the susceptibility, specific heat and magnetization
for the compound Cu$_{3}$(CO$_{3}$)$_{2}$(OH)$_{2}$ are fairly compared with
our TMRG results.
