Most of these model systems involve anisotropy or frustration. The magnetization jump was first proposed by Néel 7 in the system with the Ising-like anisotropic exchange interaction, and then also investigated in various of lattice spin systems in different dimensions 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
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The other is the magnetization jump, which exhibits discontinuity in the magnetization density. One is the magnetization plateau, which usually accompanies with the spin excitation gap and has been found in many systems, such as the frustrated spin systems 3, 4, and quasi-periodic systems with nontrivial topological property 5, 6. Among them two kinds of nonanalytic magnetization behaviors have attracted many interests. Typically, subjected to external magnetic field, the magnetization process of the spin systems can exhibit anomalous phenomena. Quantum spin systems play a very important role in condensed matter physics, because of their underlying rich physics, such as the spin liquid state 1 and the valence-bond solid (VBS) state 2. We also demonstrate that while the experienced states are Heisenberg-like without long-range order, all the jumped-over states have antiferromagnetic or Néel long-range orders, or their mixing.
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By examining the energy per magnon and the correlation function, we find that the origin of the magnetization jump is the condensation of magnons and the formation of magnetic domains. For a fixed nonzero pair coupling Q, (i) when g −1 but still small, the whole magnetization curve is continuous and smooth (iii) if further increasing g, there is a macroscopic magnetization jump from partially- to fully-polarized state (iv) for a sufficiently large g, the magnetization jump is from non- to fully-polarized state. According to the characteristic of the magnetization curves, we draw a magnetization phase diagram consisting of four phases.
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We investigate the adiabatic magnetization process of the one-dimensional J − Q 2 model with XXZ anisotropy g in an external magnetic field h by using density matrix renormalization group (DMRG) method.