Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder

Abstract

The ground-state behaviour of the frustrated quantum spin-1/2 two-leg ladder with the Heisenberg intra-rung and Ising inter-rung interactions is examined in detail. The investigated model is transformed into the quantum Ising chain with composite spins in an effective transverse and longitudinal field by employing either the bond-state representation or the unitary transformation. It is shown that the ground state of the Heisenberg–Ising ladder can be descended from three exactly solvable models: the quantum Ising chain in a transverse field, the ‘classical’ Ising chain in a longitudinal field or the spin-chain model in a staggered longitudinal–transverse field. The last model serves in evidence of the staggered bond phase with alternating singlet and triplet bonds on the rungs of a two-leg ladder, which appears at moderate values of the external magnetic field and consequently leads to a fractional plateau at a half of the saturation magnetization. The ground-state phase diagram totally consists of five ordered and one quantum paramagnetic phase, which are separated from each other either by the lines of discontinuous or continuous quantum phase transitions. The order parameters are exactly calculated for all five ordered phases and the quantum paramagnetic phase is characterized through different short-range spin–spin correlations.