Density-matrix renormalization group study of the spin-Peierls instability in the antiferromagnetic Heisenberg ladder

The columnar dimerized antiferromagnetic S = 1/2 spin ladder is numerically studied by the density-matrix renormalization-group (DMRG) method. The elastic lattice with spin-phonon coupling α and lattice elastic force k is introduced into the system. Thus the S = 1 / 2 Heisenberg spin chain is unstable towards dimerization (the spin-Peierls transition). However, the dimerization should be suppressed if the rung coupling J⊥ is sufficiently large, and a Columnar dimer to Rung singlet phase transition takes place. After a self-consistent calculation of the dimerization, we determine the quantum phase diagram by numerically computing the singlet-triplet gap, the dimerization amplitude, the order parameters, the rung spin correlation and quantum entropies. Our results show that the phase boundary between the Columnar dimer phase and Rung singlet phase is approximately of the form J⊥ ~ \hbox{$(\frac{k}{\alpha^{2}})^{-\frac{5}{4}}$} ( k α 2 ) − 5 4.