We investigate the ground-state phase diagram of a frustrated spin-1/2 Heisenberg ladder in the transverse magnetic field with an anisotropic inter-rung exchange coupling
α. This bond-anisotropic parameter continuously interpolates among the Ising-like limit
α=0, the isotropic point
α=1, and the XY-dominated regime
α≫1. Using density-matrix renormalization group calculations within a matrix-product-state framework, we analyze bipartite entanglement, magnetization, and spin correlations to characterize the emergent quantum phases. We identify six distinct ground-state phases, including rung-singlet, Haldane-like, Tomonaga-Luttinger liquid, canted Ising-ordered, XY-polarized, and ordered ferromagnetic states. While magnetization and local correlations provide a first insight into phase classifications, the finite-size scaling of the entanglement measures offers a more sensitive and unified diagnostics of both gapped and gapless regimes. In the gapless regime, we extract the central charge
c≃1, confirming Tomonaga-Luttinger liquid behavior, while at the transition between the canted Ising and ferromagnetic phases, we observe
c≃1/2, consistent with the Ising universality. Finally, we find that both the Haldane-like behavior and the extended critical Tomonaga-Luttinger liquid regime are strongly confined to the vicinity of the isotropic point
α=1.
In this work, we study alternating mixed-spin (s,S) Heisenberg ladders in the magnetic field h density matrix renormalization group and linear spin-wave calculations. The h versus interchain coupling J_{⊥} phase diagram for the (1/2,1) case is investigated in detail. In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of J_{⊥} and of h along the chain, J_{⊥} and h scans, and considering the usual case of chains with uniform couplings. The magnetization plateau at 1/3 of saturation magnetization, 1/3 plateau, is observed for J_{⊥}>0 and in a limited range for J_{⊥}<0. The critical Kosterlitz-Thouless transition point, where the 1/3 plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.
We use density-matrix renormalization group to study the first-order quantum phase transition induced by a magnetic field
h in a frustrated ferrimagnetic chain. The magnetization (
m) curve as a function of
h presents a macroscopic jump and the energy curve as a function of
m has two global minima. We characterize the two competing phases and study the phase-separated states in the coexistence region. Also, we observe that the transition is accompanied by an increase in the number of itinerant singlet pairs between sites in the unit cells of the chain. Finally, we identify the critical point at the end of the first-order transition line and a crossover line.
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.
We study the magnetic phase diagram of two coupled mixed-spin
(1,21) Heisenberg chains as a function of the frustration parameter related to diagonal exchange couplings. The analysis is performed by using spin-wave series and exact numerical diagonalization techniques. The obtained phase diagram---containing the Luttinger liquid phase, the plateau phase with a magnetization per rung
M=1∕2, and the fully polarized phase---is closely related to the generic $(J∕U,\ensuremath{\mu}∕U)$ phase diagram of the one-dimensional boson Hubbard model.
Quantum many-body edge and extended magnon excitations from the 1/3 plateau of the anisotropic Heisenberg model on an open
AB2 chain in a magnetic field
h are unveiled using the density matrix renormalization group and exact diagonalization. By tuning both the anisotropy and
h in the rich phase diagram, the edge states penetrate in the bulk, whose gap closes in a symmetry-protected topological Kosterlitz-Thouless transition. Also, we witness the squeezed chain effect, the breaking of the edge state degeneracy, and a topological change of the excitations from gapped magnons with quadratic long-wavelength dispersion to a linear spinon dispersion in the Luttinger liquid gapless phase as the anisotropy $\ensuremath{\lambda}$ approaches the critical point from the $\ensuremath{\lambda}>0$ side of the phase diagram.