Competing phases in spin ladders with ring exchange and frustration

The ground-state properties of spin-1/2 ladders are studied, emphasizing the role of frustration and ring exchange coupling. We present a unified field theory for ladders with general coupling constants and geometry. Rich phase diagrams can be deduced by using a renormalization group calculation for ladders with in-chain next-nearest-neighbor interactions and plaquette ring exchange coupling. In addition to established phases such as Haldane, rung singlet, and dimerized phases, we also observe a surprising instability towards an incommensurate phase for weak interchain couplings, which is characterized by an exotic coexistence of self-consistent ferromagnetic and antiferromagnetic order parameters.

Figure 1

Generalized spin ladder with ring exchange interaction $K$, NNN coupling $J_2$, and two diagonal couplings $J_d$ and $J_d^{\prime }$.

Figure 2

Phase diagram of the cross coupled ladder as a function of $K$, and the ratio $J_{\perp }/2J_d$, for $J_d=J_d^{\prime }=0.2J$, and three values of $J_2=0,0.2J$, and $J_{2c}$, denoted by black solid, blue dashed, and red dot-dashed lines, respectively.

Figure 3

Phase diagram of the diagonal ladder $\left(J_d^{\prime }=0\right)$ as a function of $J_d$ and $J_{\perp }$ for $K=0$ and three values of $J_2=0,0.2J$, and $J_{2c}$, denoted by black solid, blue dashed, and red dot-dashed lines respectively.

Figure 4

Phase diagram of the diagonal ladder $\left(J_d^{\prime }=0\right)$ as a function of $J_d$ and $K$ for $J_{\perp }/J_d=1.1$ and $J_2=0.2J$.

Figure 5

Phase diagram as a function of $-J_d^{\prime }/J_d$ and $K$, for $J_{\perp }=0,J_2=J_{2c}$, and $J_d=0.2J$.