Magnetization plateaus, Haldane-like gap, string order, and hidden symmetry in a spin-12tetrameric 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, respectively͒ are studied by means of the density-matrix renormalization-group method. Two plateaus 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 ϫ 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.

Magnetism and thermodynamics of spin-(12,1)decorated Heisenberg chain with spin-1 pendants

“…2 and 3͒ and DMRG. 20,21 During the DMRG calculations, the chain length is taken as L = 300, and the Hilbert space is truncated to 240 most relevant states. Open boundary conditions are adopted and the truncation error is less than 10 −8 in all calculations.…”

Ground state fidelity in bond-alternative Ising chains with Dzyaloshinskii–Moriya interactions

“…Quantum phase transitions driven by stronger quantum fluctuations then exhibit more interesting and novel quantum phenomena in lowdimensional spin systems. The effects of alternating bond interactions, especially, have been intensively studied theoretically in spin systems such as antiferromagnetic Heisenberg chains [3][4][5][6][7][8], Heisenberg chains with next-nearest-neighbor bond alternations [9,10], a tetrameric Heisenberg antiferromagnetic chain [11], and two-leg spin ladders [12,13]. A recent experiment has demonstrated a realization of a bond-alternating chain by applying magnetic fields in a spin-1/2 chain antiferromagnet [14].…”