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arXiv:1109.4078 · Physical Review B

Supersolid phase and magnetization plateaus observed in the anisotropic spin- 32 Heisenberg model on bipartite lattices

Judit Romhányi, Frank Pollmann, Karlo Penc

Published Nov 17, 2011• 19 citations
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Abstract

We study the spin-$3/2$ Heisenberg model including easy-plane and exchange anisotropies in one and two dimensions. In the Ising limit, when the off-diagonal exchange interaction $J$ is zero, the phase diagram in magnetic field is characterized by magnetization plateaus that are either translationally invariant or have a two-sublattice order, with phase boundaries that are macroscopically degenerate. Using a site-factorized variational wave function and perturbational expansion around the Ising limit, we find that superfluid and supersolid phases emerge between the plateaus for small finite values of $J$. The variational approach is complemented by a density matrix renormalization group study of a one-dimensional chain and exact diagonalization calculations on small clusters of a square lattice. The studied model may serve as a minimal model for the layered Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ material compound, and we believe that the vicinity of the uniform 1/3 plateau in the model parameter space can be observed as an anomaly in the measured magnetization curve.

DOI
10.1103/physrevb.84.184427

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We examine ground-state properties of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice with ferromagnetic transverse spin exchange using quantum Monte Carlo and degenerate perturbation theory. For vanishing transverse exchange, the model reduces to an antiferromagnetic Ising model that, besides N\'eel order, harbors regions of extensive ground-state degeneracy. In the quantum regime, we find a dimerized phase of triplet states separated from the N\'eel ordered phase by a superfluid. The quantum phase transitions between these phases are characterized. The magnetization process shows a magnetization plateau at 1/3 of the saturation value, which persists down to the Ising limit, and a further plateau at 1/2 only in the quantum regime. For both plateaus, we determine the crystalline patterns of the localized triplet excitations. No further plateaus or supersolid phases are found in this model.
We present a systematic numerical study of the spin-1 antiferromagnetic Heisenberg model on the triangular lattice in an out-of-plane magnetic field, using Density Matrix Renormalization Group (DMRG) methods. By mapping out the quantum phase diagram as a function of the single-ion anisotropy DzD_zDz​ and magnetic field, we identify distinct dipolar and quadrupolar spin supersolid states, characterized by spontaneous U(1) symmetry breaking with finite spin superfluid stiffness coexisting with longitudinal translational symmetry breaking. At zero field, the dipolar spin supersolid with a 'Y'-type spin configuration persists down to Dz=0D_z = 0Dz​=0, whereas the quadrupolar spin supersolid prevails at large DzD_zDz​. At intermediate fields, the phase diagram is dominated by an up-up-down phase. At high fields below saturation, a quadrupolar spin superfluid emerges in the large-DzD_zDz​ regime, whereas a dipolar spin supersolid with a 'V'-type spin configuration dominates at small DzD_zDz​. These phases are characterized through their order parameters and spin superfluid stiffness using calculations on various system sizes. Furthermore, the dynamical spin structure factor is obtained across the phase diagram, where characteristic spectral signatures of different phases are observed, including the gapless Goldstone mode and the roton-like minima. These features are directly accessible to inelastic neutron scattering experiments. Our results provide a theoretical understanding of the interplay between frustrations, anisotropy, and Zeeman interactions in driving distinct spin supersolid phases in the spin-1 system, which are relevant to various triangular-lattice antiferromagnets such as Na2_22​BaNi(PO4_44​)2_22​ and K2_22​Ni(SeO3_33​)2_22​.
We investigate the S=1S=1S=1 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using numerical exact diagonalization of finite-size clusters, level spectroscopy analysis, and the density matrix renormalization group (DMRG). We find that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase.
Magnetization plateaus in quantum spin systems emerges in two-dimensional frustrated systems such as kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice is also appropriate for the study of magnetization plateau. Motivated by recent experimental finding of such a square-kagome lattice with nonequivalent three bonds, we investigate the phase diagrams and magnetization plateaus of the lattice by the exact diagonalization method. In addition to previously reported the 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.
We explore the field-induced magnetic phases of an S=1S=1S=1 XXZXXZXXZ model with single-ion anisotropy and large Ising-like anisotropy on a Shastry-Sutherland lattice over a wide range of Hamiltonian parameters and applied magnetic field. The multitude of ground-state phases are characterized in detail in terms of their thermodynamic properties, and the underlying classical (Ising limit) spin arrangements for the plateau phases are identified by calculating the static structure factors. The enlarged local Hilbert space of the S=1S=1S=1 spins results in several ground state phases that are not realized for S=1/2S=1/2S=1/2 spins. These include the quantum paramagnetic state that is ubiquitous to S=1S=1S=1 spins with single-ion anisotropy, two different spin supersolid phases (with distinct longitudinal ordering), and a magnetization plateau that arises as a direct descendant of the 1/3 plateau due to quantum fluctuations that are not possible for S=1/2S=1/2S=1/2 spins. We predict the same mechanism will lead to plateaus at smaller fractions of 1/3 for higher spins. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order as well as the different longitudinal orderings.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.