Thermodynamic Density Matrix Renormalization Group Study of the Magnetic Susceptibility of Half-Integer Quantum Spin Chains

It is shown that White's density matrix renormalization group technique can be adapted to obtain thermodynamic quantities. As an illustration, the magnetic susceptibility of Heisenberg $S=1\mathrm{}/2$ and $S=3\mathrm{}/2$ spin chains are computed. A careful finite size analysis is made to determine the range of temperatures where the results are reliable. For the $S=1\mathrm{}/2$ chain, the comparison with the exact Bethe ansatz curve shows an agreement within $1\%$ down to $T=0.05J$.