Low-Lying Energy Properties of a Frustrated Antiferromagnetic Spin-$\frac{1}{2}$ Ladder

Abstract

Using the Density Matrix Renormalization Group method, we determined the phase diagram of a frustrated antiferromagnetic spin-$\frac{1}{2}$ ladder at zero temperature. Two spin-gapped phases, the Haldane phase and the singlet phase, are identified. A phase transition between the two phases occurs at any non-zero value of frustration coupling $J_{\times }$. On the phase boundary, the spin gap vanishes for sufficiently small $J_{\times }$. Crossing this non-gapped line, the transition is of second order, while of first order for larger $J_{\times }$. Striking frustration effects are predicted for ladder materials.

8 pages, 6 figures, Revtex