Magnetization plateaux, Haldane-like gap, string order and hidden symmetry in a spin-1/2 tetrameric Heisenberg antiferromagnetic chain

Abstract

The ground-state properties of a spin $S=1/2$ tetrameric Heisenberg antiferromagnetic chain with alternating couplings AF${}_1$-AF${}_2$-AF${}_1$% -F (AF and F denote antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the density matrix renormalization group method. Two plateaux of magnetization $m$ are found at $m=0$ and 1/4% . It is shown that in such a spin-1/2 AF system, there is a gap from the singlet ground state to the triplet excited states in the absence of a magnetic field. The spin-spin correlation function decays exponentially, and the gapped states have a nonvanishing string order, which measures a hidden symmetry in the system. By a dual transformation, the string order is transformed into a ferromagnetic order and the hidden symmetry is unveiled to be a $Z_2\times Z_2$ discrete symmetry, which is fully broken in the gapped states. This half-integer spin Heisenberg AF chain is in a Haldane-like phase, suggesting that the present findings extend the substance of Haldane's scenario. A valence-bond-solid state picture is also proposed for the gapped states.

11pages, 7 figures

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Cited by in corpus (12)

• Thermal entanglement of one-dimensional Heisenberg quantum spin chains in magnetic fields
• Thermodynamics of spin-1/2 tetrameric Heisenberg antiferromagnetic chain
• Phase Diagrams, Distinct Conformal Anomalies and Thermodynamics of Spin-1 Bond-Alternating Heisenberg Antiferromagnetic Chain in Magnetic Fields
• Magnetism and thermodynamics of spin-(1/2,1) decorated Heisenberg chain with spin-1 pendants
• Magnetization plateau and incommensurate spin modulation in Ca3Co2O6
• Ground state fidelity in bond-alternative Ising chains with Dzyaloshinskii-Moriya interactions
• Spatial Reflection and Associated String Order in Quantum Spin Chains
• Quantum phase transitions in a spin-1/2 alternating Heisenberg antiferromagnetic chain under a staggered transverse magnetic field
• Translational symmetry broken magnetization plateau of the S=1 antiferromagnetic Heisenberg chain with competing anisotropies
• Spin nematic states in antiferromagnets containing ferromagnetic bonds
• Translational-Symmetry-Broken Magnetization Plateaux of the $S=3/2$ Anisotropic Antiferromagnetic Chain
• Spin order, spin excitations, and RIXS spectra of spin-1/2 tetramer chains