At zero temperature, thermal fluctuation is eliminated and phase transitions will occur due to quantum fluctuations that arise from the Heisenberg uncertainty principle. Magnetic insulators, described by the Heisenberg model Hamiltonian, are a known class of physical systems that can undergo quantum phase transitions when submitted to a magnetic field. The magnetic field induces the transition by closing energy gaps through the Zeeman effect. Examples of systems that undergo these transitions are the antiferromagnetic spin-1 chain, the antiferromagnetic spin- 1/2 ladder, the ferrimagnetic mixed spin-1 and spin- 1/2 chains and ladders. The presence of a gap in the energy spectrum with zero magnetic field leads to a magnetization plateau in the magnetization curve. We use the density matrix renormalization group to investigate the magnetization curves of the mixed spin-1 and spin- 1/2 ladder, for antiferromagnetic and ferro- magnetic couplings between the ladder legs J⊥. For J⊥ > 0, the ground-state is ferrimagnetic with the total spin equal to 1/3 of the saturation value, in accord with the Lieb-Mattis theorem. The magnetization curve presents a plateau at total magnetization 1/3 of the saturation value, the 1/3-plateau since the ground state has a gap to excitations that increase the total spin by 1 unit. Decreasing J⊥ below zero, the ground state becomes a singlet, but the 1/3-plateau survives down to a critical value J⊥ = Jc. Given that the gap closes with the magnetization fixed, it is a Kosterlitz-Thouless transition type. To determine Jc, we have made a finite-size scale analysis of the plateau width.
Spin-
21 two-leg ladder models under a magnetic field have a well-known phase diagram. In this paper, we use multipartite nonlocality (a measure of multipartite quantum correlations) to characterize the quantum correlations in the ladder models at zero temperature. Both finite-size and infinite-size ladders are considered. We investigate the global nonlocality ${\mathcal{S}}_{g}=\mathcal{S}(|{\mathrm{\ensuremath{\Psi}}}_{g}\ensuremath{\rangle})$, which describes quantum correlations of the ground states $|{\mathrm{\ensuremath{\Psi}}}_{g}\ensuremath{\rangle}$ of the entire lattices, and the partial nonlocality ${\mathcal{S}}_{p}=\mathcal{S}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{n})$, which describes quantum correlations of the reduced states ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{n}$ of some sublattices in the ladders. We find that as the magnetic field $\ensuremath{\lambda}$ increases, the global nonlocality
Sg presents a single-peak curve. Moreover, the logarithmic measure
lnSg changes dramatically at the two critical fields ${\ensuremath{\lambda}}_{{c}_{1}}$ and ${\ensuremath{\lambda}}_{{c}_{2}}$ of the models and thus signals the quantum phase transitions in the models. For the partial nonlocality
Sp, in the regions ${\ensuremath{\lambda}}_{{c}_{1}}<\ensuremath{\lambda}<{\ensuremath{\lambda}}_{{c}_{2}}$, we observe that the ${\mathcal{S}}_{p}(\ensuremath{\lambda})$ curve shows an oscillation. Numerical results reveal that the underling mechanism is the ``major component transitions'' in the reduced states ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}}_{n}$ of the sublattices. More importantly, the oscillation of the partial nonlocality
Sp is modulated by the single-peak curve of the global nonlocality
Sg. The result provides valuable clues about the relation between partial nonlocality and global nonlocality in low-dimensional quantum models.