We study finite-temperature magnetization transport in a one-dimensional anisotropic Heisenberg model, focusing in particular on the gapped phase. Using numerical simulations by two different methods, a propagation of localized wavepackets and a study of nonequilibrium steady states of a master equation in a linear-response regime, we conclude that the transport at finite temperatures is diffusive. With decreasing temperature the diffusion constant increases, possibly exponentially fast. This means that at low temperatures the transition from ballistic to asymptotic diffusive behavior happens at very long times. We also study dynamics of initial domain wall like states, showing that on the attainable time scales they remain localized.
Magnetization curves of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are calculated with the help of density-matrix renormalization group method for several quantum spin numbers S=1, 3/2, 2 and 5/2. It is shown that the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains exhibit irrespective of the spin value S exactly one intermediate magnetization plateau, which can be identified with the gapped Lieb-Mattis ferrimagnetic ground state. The magnetization plateau due to the Lieb-Mattis ferrimagnetism breaks down at a quantum phase transition towards the Luttinger spin liquid, which is …
An $S=1/2$ triangular-lattice Heisenberg antiferromagnet with next-nearest-neighbor interactions is investigated under a magnetic field by the numerical-diagonalization method. It is known that, in both cases of weak and strong next-nearest-neighbor interactions, this system reveals a magnetization plateau at one-third of the saturated magnetization. We examine the stability of this magnetization plateau when the amplitude of next-nearest-neighbor interactions is varied. We find that a nonplateau region appears between the plateau phases in the cases of weak and strong next-nearest-neighbor in…
Ground-state phase diagrams and magnetization curves of a spin-1 Heisenberg diamond cluster with two different coupling constants and uniaxial single-ion anisotropy are investigated in a presence of the external magnetic field with the help of exact diagonalization methods. It is shown that the spin-1 Heisenberg diamond cluster exhibits several remarkable quantum ground states, which are manifested in zero- and low-temperature magnetization curves as intermediate plateaus at one-quarter, one-half and three-quarters of the saturation magnetization. It is found that the width of the fractional m…
The magnetization curves and magnetocaloric effect during the adiabatic demagnetization of antiferromagnetic spin-1/2 $XXZ$ Heisenberg clusters with the shape of Johnson's solids (triangular cupola, square cupola and pentagonal cupola) are investigated using the exact numerical diagonalization for different values of the exchange anisotropy ranging in between the Ising and fully isotropic limit. It is demonstrated that spin-1/2 $XXZ$ Heisenberg cupolae display, in comparison with their Ising counterparts, at least one more magnetization plateau. The novel magnetization plateaux extends over a …
Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered within the many-body perturbation theory developed from the exactly solved spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising interdimer interactions. The former model is widely used for a description of magnetic properties of the layered compound SrCu$_2$(BO$_3$)$_2$, which exhibits a series of fractional magnetization plateaux at sufficiently low temperatures. Using the novel type of many-body perturbation theory we have found the effective model of interacting triplet excitations with the extende…
Bond Operator Mean Field Approach to the Magnetization Plateaux in Quantum Antiferromagnets -- Application to the S=1/2 Coupled Dimerized Zigzag Heisenberg Chains
We establish a solvable Heisenberg-Ising model on a spin-1 Ni-containing polymer chain, $[Ni (NN'-dmen) (μ-N_3)_2]$, with $NN'-dmen$ being $NN'-dimethylethylenediamine$, that fully covers the interaction characteristics of the material and by which, we can characterize all the peculiar magnetic features of the polymer, which has been partly studied in experiment. By purely analytical calculations, we can see that the magnetization exhibits three plateaus at zero, mid, and 3/4 of the saturation value at low temperatures below 2 K. The corresponding featuring peaks of magnetic susceptibility are…
We investigate the time dynamics of quantum correlations of the anisotropic Heisenberg model in a time-dependent magnetic field, in one-dimensional, ladder, and two-dimensional lattices. We find that quantum correlation measures in the entanglement-separability paradigm are ergodic in these systems irrespective of system parameters. However, information-theoretic quantum correlation measures can also be nonergodic, and exhibit a transition from nonergodic to ergodic behavior with the change of interaction strength in the direction of the magnetic field. We also observe that the transition poin…
We investigate the $S=2$ antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at a half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetizat…
A full energy spectrum, magnetization and susceptibility of a spin-1/2 Heisenberg model on two edge-shared tetrahedra are exactly calculated by assuming two different coupling constants. It is shown that a ground state in zero field is either a singlet or a triplet state depending on a relative strength of both coupling constants. Low-temperature magnetization curves may exhibit three different sequences of intermediate plateaux at the following fractional values of the saturation magnetization: 1/3-2/3-1, 0-1/3-2/3-1 or 0-2/3-1. The inverse susceptibility displays a marked temperature depende…
The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S=1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.
We study the magnetization process of the spin-$1/2$ Heisenberg antiferromagnet on a distorted square-kagome lattice by the numerical-diagonalization method. The magnetization jump at one-third of the height of the saturation is examined in detail; we find that the jump becomes larger when a small distortion is switched on and that it is accompanied by an abrupt change in lines along microscopic spin directions. Our finite-size results successfully confirm that the magnetization jump in a spin-isotropic system is a macroscopic jump that survives in the thermodynamic limit and that the changes …
The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp".
Magnetization plateaus and enhanced magnetocaloric effect of a spin-1/2 Ising-Heisenberg and Heisenberg double sawtooth ladder with four-spin interaction
We consider the magnetic-field dependent spatial magnetization pattern around a general impurity embedded in a Heisenberg antiferromagnet using both an analytical and a numerical spin wave approach. The results are compared to quantum Monte Carlo simulations. The decay of the magnetization pattern away from the impurity follows a universal form which reflects the properties of the pure antiferromagnetic Heisenberg model. Only the overall magnitude of the induced magnetization depends also on the size of the impurity spin and the impurity coupling.
We apply the coupled cluster method and exact diagonalzation to study the uniform susceptibility and the ground-state magnetization curve of the triangular-lattice spin-1 Heisenberg antiferromagnet. Comparing our theoretical data for the magnetization curve with recent measurements on the s=1 triangular lattice antiferromagnet Ba3NiSb2O9 we find a very good agreement.
The ground state and magnetization process of an exactly solved spin-$1/2$ Ising-Heisenberg orthogonal-dimer chain with two different gyromagnetic factors of the Ising and Heisenberg spins are investigated in detail. It is shown that the investigated quantum spin chain exhibits up to seven possible ground states depending on a mutual interplay of the magnetic field, intra- and inter-dimer coupling constants. More specifically, the frustrated and modulated quantum antiferromagnetic phases are responsible in zero-temperature magnetization curves for a zero magnetization plateau. The intermediate…
We study the S=1/2 Heisenberg antiferromagnet on the Cairo pentagon lattice by the numerical-diagonalization method. We tune the ratio of two antiferromagnetic interactions coming from two kinds of inequivalent sites in this lattice, examining the magnetization process of the antiferromagnet; particular attention is given to one-third of the height of the saturation. We find that quantum phase transition occurs at a specific ratio and that a magnetization plateau appears in the vicinity of the transition. The plateau is accompanied by a magnetization jump on one side among the edges due to the…
We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.
We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to $S=9/2$. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly $c$, the sound velocity $v_{s}$, the anomalous dimension $x_{bulk}$, and the surface exponent $x_{s}$ of the anisotropic spin-$S$ Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop $S(L,l_{A},S)$ of t…
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
We analyze theoretically the novel pathway of ultrafast spin dynamics for ferromagnets with high enough single-ion anisotropy (non-Heisenberg ferromagnets). This longitudinal spin dynamics includes the coupled oscillations of the modulus of the magnetization together with the quadrupolar spin variables, which are expressed through quantum expectation values of operators bilinear on the spin components. Even for a simple single-element ferromagnet, such a dynamics can lead to an inertial magnetization reversal under the action of an ultrashort laser pulse.
The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagona…
We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaux for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its saturation value. These incompressible states correspond to somehow similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for m=0. Our results are based on Exact Diagonalization as well as Density Matrix Renormalization Group large-scale simulations, and interpreted in terms of simple trial w…
The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the perturbative strong-coupling approach, which is developed from the exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg intradimer and the Ising interdimer couplings. Although the spin-1/2 Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaux at zero, one-quarter and one-half of the saturation magnetization, the perturbative treatment up to second order stemming from this exactly solvable model additionally corroborates the fractional one-third plateau as well as the gap…
The quantum spin-1/2 orthogonal-dimer chain with the Heisenberg intra-dimer and Ising inter-dimer interactions in a magnetic field is considered by a rigorous approach. The model conserves the z-component of total spin on vertical Heisenberg bonds and this property is used to calculate exactly the partition function using the transfer-matrix method. We have found the ground-state phase diagram of the given model in a magnetic field as well as the macroscopic degeneracy along field-induced transitions accompanied with the magnetization jumps. The model exhibits two intermediate fractional plate…
The magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the 1/3 and 2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the 1/3 plateau are obtained by using the approximated state in the unit cell and compared with the nu- merical results of the exact diagonalization of 42 sites.
We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size perio…
In this study, we investigate the magnetic susceptibility, entropy, and isothermal magnetization curve of the spin-1/2 Heisenberg model on an anisotropic triangular lattice using the orthogonalized finite-temperature Lanczos method. In addition, we investigate the adiabatic magnetization curve and magnetocaloric effect. We estimate these physical quantities with sufficient accuracy in the thermodynamic limit, except at low temperatures. We observe a 1/3 magnetization plateau in the isothermal magnetization process, whereas the plateau is observed to have a slope in the adiabatic process. We sh…
The magnetization process of the S=1/2 Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. We successfully obtain a new result of the magnetization process of a 42-site cluster in the entire range. Our analysis clarifies that the critical behavior around one-third of the height of the saturation is different from the typical behavior of the well-known magnetization plateau in two-dimensional systems. We also examine the effect of the $\sqrt{3}\times\sqrt{3}$-type distortion added to the kagome lattice. We find at one-third of the height of the s…
We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Delta is varied spin transport changes from ballistic for Delta<1 to anomalous at the isotropic point Delta=1, to diffusive for finite Delta>1, ending up as a perfect isolator in the Ising limit of infinite Delta. Using perturbation theory for large Delta a quantitative prediction is made for the dependence of diffusion constant on Delta.
We use the spin functional renormalization group recently developed by two of us [J. Krieg and P. Kopietz, Phys. Rev. B $\bf{99}$, 060403(R) (2019)] to calculate the magnetization $M ( H , T )$ and the damping of magnons due to classical longitudinal fluctuations of quantum Heisenberg ferromagnets. In order to guarantee that for vanishing magnetic field $H \rightarrow 0$ the magnon spectrum is gapless when the spin rotational invariance is spontaneously broken, we use a Ward identity to express the magnon self-energy in terms of the magnetization. In two dimensions our approach correctly predi…
We study the S=1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the long-range-ordered ground state with this structure exists in the range of 0.7 \simle J_2/J_1 \le 1, where J_1 is the interaction amplitude along the chains and J_2 is the amplitude of other interactions.
An exact analytical solution of the ground state problem of the isotropic classical Heisenberg model on the Shastry-Sutherland lattice in external magnetic field $H$ is found for arbitrary ratio of diagonal to edge exchange constants $J_2/J_1$. The phase diagram of this model in the ($J_2/J_1, H/J_1$) plane is presented. It includes spin-flop, spin-flip and umbrella phases. The magnetization curves are found to be linear until saturation. It is shown numerically that the inclusion of the easy-axis anisotropy into the model leads to the appearance of the 1/3 magnetization plateau, corresponding…
We study the magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on a layered triangular lattice by means of a numerical cluster mean-field method with a scaling scheme (CMF+S). It has been known that antiferromagnetic spins on a two-dimensional (2D) triangular lattice with quantum fluctuations exhibit a one-third magnetization plateau in the magnetization curve under magnetic field. We demonstrate that the CMF+S quantitatively reproduces the magnetization curve including the stabilization of the plateau. {We also discuss the effects of a finite interlayer coupling, which …
Spin-1/2 Heisenberg model on kagome lattice is a typical frustrated quantum spin system. A basic structure of kagome lattice is also present in kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-1/2 Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions by the density-matrix renormalization group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking either translati…
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 …
We have performed high-field magnetization and ESR measurements on Ba$_3$CoSb$_2$O$_9$ single crystals, as a representative two-dimensional spin-1/2 Heisenberg antiferromagnet on a uniform triangular lattice, and have determined all the magnetic parameters. For an applied magnetic field $H$ parallel to the $ab$-plane, the entire magnetization curve including the plateau at one-third of the saturation magnetization ($M_\mathrm{s}$) is in excellent agreement with the results of theoretical calculations except an anomaly near $(3/5)M_\mathrm{s}$, indicative of an additional field-induced transiti…
