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

Abstract

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 to 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 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 disordered 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 disordered phase is characterized through different short-range spin-spin correlations.

corrected version, figure A1 has been changed, accepted in J. Phys. A, 19 pages, 7 figures

References in corpus (7)

• Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• Effect of temperature on quantum criticality in the frustrated two-leg Heisenberg ladder
• Exact magnetization plateaus and phase transitions in spin-S Heisenberg antiferromagnets in arbitrary dimensions
• Quantum and classical criticalities in the frustrated two-leg Heisenberg ladder
• Interplay between field-induced and frustration-induced quantum criticalities in the frustrated two-leg Heisenberg ladder

Cited by in corpus (3)

• Interplay between spin frustration and thermal entanglement in the exactly solved Ising-Heisenberg tetrahedral chain
• Ground state of a spin-1/2 Heisenberg-Ising two-leg ladder with XYZ intra-rung coupling
• On the compressibility of deformable spin chains in a vicinity of quantum critical points