Quantum phase transitions in a spin ladder with long-range couplings

An integrable model with rich ground state phases is difficult to realize. In this paper, an integrable spin ladder with pure long-range Heisenberg couplings is proposed and solved via the asymptotic Bethe ansatz method. Numerical solutions of the Bethe ansatz equation show that with the variation of the coupling range parameter α, quantum phase transitions exist for both ferromagnetic (J=-1) and antiferromagnetic (J=1) intrachain couplings. For J=-1, depending on α, the ground state may be ferromagnetic, Takhtajan-Babujian spin liquid, or a frustrated spin liquid. For J=1, a quantum phase transition from the Heisenberg spin liquid to an exotic spin liquid occurs at a critical α. The phase boundaries are determined numerically.