Spin-Peierls Instability in the Ferromagnetic Heisenberg Ladder

A two-leg S=1/2 spin ladder with ferromagnetic rung coupling is investigated to reveal the phase transition between the Haldane and columnar dimer phase. The elastic lattice with the elastic force K is introduced into the system, which induces unstable spin chains towards the spontaneous dimerization. When the rung coupling is strong enough, the dimerization along the legs is suppressed and the spin ladder undergoes a phase transition. The dimerization amplitude is calculated self-consistently by the density-matrix renormalization group method. To determine the phase transition boundary, the spin gap, the columnar dimer order parameter and the block-block entanglement entropy are calculated. Our results show that the phase boundary between the columnar dimer phase and Haldane phase follows the power law J_t～K^?α.