Mixed-spin Heisenberg Research Articles

Ground-state phase diagram and universality of sequential topological valence-bond-solid quantum transitions in a mixed tetramer chain

The ground-state ordering of a quantum mixed-spin Heisenberg tetramer chain composed of an alternate sequence of s = 1 and S=3/2 dimers is studied in detail as a function of two considered exchange interactions ascribed to similar and dissimilar spin pairs. At zero magnetic field, the ferrimagnetic mixed spin-(1, 1, 3/2, 3/2) Heisenberg tetramer chain displays, depending on a mutual interplay between two considered exchange interactions, three distinct gapped valence-bond-solid phases separated by gap-closing quantum critical points. Using density-matrix renormalization group calculations we construct the full ground-state phase diagram as a function of the interaction ratio and magnetic field, which exhibits besides three gapped valence-bond-solid phases special Kosterlitz–Thouless and topological quantum critical points. A tangential finite-size scaling analysis is employed to obtain precise estimates of the zero-field valence-bond-solid transitions and unveil their common logarithmic correction to a power-law scaling of the correlation length.

Local quantum Fisher information and quantum correlation in the mixed-spin Heisenberg XXZ chain

Local quantum Fisher information and quantum correlation in the mixed-spin Heisenberg XXZ chain

Topological quantum phase transition in a mixed-spin Heisenberg tetramer chain with alternating spin-1/2 and spin-5/2 dimers

We investigate magnetic quantum phases and the topological quantum phase transition between two distinct valence-bond solid (VBS) phases of a minimal interacting spin-chain model that captures a magnetic behavior of the novel low-dimensional quantum ferrimagnetic material Cu2Fe2Ge4O13. The studied mixed-spin Heisenberg tetramer chain consists of a 4-period array of spins involving two types of dimers sa−sa (sa=1/2) and Sb−Sb (Sb=5/2) under the assumption of unique intra- and inter-dimer coupling constants J1 and J2, respectively. Using the tensor-network formulation of the density-matrix renormalization group method, we have constructed the ground-state phase diagram in the parameter space magnetic field versus the interaction ratio J=J2/J1, whereby all ground states are in accordance with the Oshikawa–Yamanaka–Affleck theorem for a given period. In addition, we have implemented the recent tangential finite-size scaling method in order to characterize the critical behavior of the topological VBS transition through calculation of the critical point Jc and the critical exponent of the correlation length ν. Our results are consistent with the topological quantum phase transition from the SU(2) Wess–Zumino–Witten universality class with the critical exponent of correlation length ν=2/3 by assuming the proper logarithmic correction.

Towards lattice-gas description of low-temperature properties above the Haldane and cluster-based Haldane ground states of a mixed spin-(1,1/2) Heisenberg octahedral chain.

The rich ground-state phase diagram of the mixed spin-(1,1/2) Heisenberg octahedral chain was previously elaborated from effective mixed-spin Heisenberg chains, which were derived by employing a local conservation of a total spin on square plaquettes of an octahedral chain. Here we present a comprehensive analysis of the thermodynamic properties of this model. In the highly frustrated parameter region the lowest-energy eigenstates of the mixed-spin Heisenberg octahedral chain belong to flat bands, which allow a precise description of low-temperature magnetic properties within the localized-magnon approach exploiting a classical lattice-gas model of hard-core monomers. The present article provides a more comprehensive version of the localized-magnon approach, which extends the range of its validity down to a less frustrated parameter region involving the Haldane and cluster-based Haldane ground states. A comparison between results of the developed localized-magnon theory and accurate numerical methods such as full exact diagonalization and finite-temperature Lanczos technique convincingly evidence that the low-temperature magnetic properties above the Haldane and the cluster-based Haldane ground states can be extracted from a classical lattice-gas model of hard-core monomers and dimers, which is additionally supplemented by a hard-core particle spanned over the whole lattice representing the gapped Haldane phase.

Exact and density matrix renormalization group studies of two mixed spin- (12,52,12) branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

The mixed-spin Ising-Heisenberg and Heisenberg branched chains whose magnetic backbone consists of regularly alternating spins 1/2 and 5/2, the latter of which are additionally coupled to an extra spin 1/2 providing lateral branching, are investigated using exact analytical and density matrix renormalization group (DMRG) methods. The proposed spin-chain models capture some relevant aspects of the heterotrimetallic coordination polymer $[\mathrm{Cu}\mathrm{Mn}(\mathrm{L})][\mathrm{Fe}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{Cl}{\mathrm{O}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$. The mixed spin-$(1/2,5/2,1/2)$ Ising-Heisenberg branched chain is exactly solvable under the assumption of an Ising-like exchange coupling along the chain, while the lateral branching is treated as an anisotropic $XXZ$ Heisenberg exchange interaction. We determine the ground-state phase diagram and quantify a bipartite quantum entanglement between dimers at lateral branching. It is shown that the studied mixed-spin Ising-Heisenberg branched chain accurately fits available experimental data for temperature dependence of the magnetic susceptibility. The ground-state phase diagram of the analogous mixed spin-$(1/2,5/2,1/2)$ Heisenberg branched chain is obtained within the DMRG method. The ground-state phase diagrams of the Ising-Heisenberg and its full Heisenberg counterpart are contrasted. In particular, the ground-state phase diagram of the mixed-spin Heisenberg branched chain involves a special Gaussian critical point, for which a proper finite-size scaling analysis is provided to accurately estimate its location and the correlation length critical exponent.

Magnetization curves of di-, tri- and tetramerized mixed spin-1 and spin-2 Heisenberg chains

Magnetization curves of ferrimagnetic mixed spin-1 and spin-2 Heisenberg chains are calculated with the help of density-matrix renormalization group method and quantum Monte Carlo simulations by considering a spin dimerization (1,2), trimerization (1,1,2) and tetramerization (1,1,1,2). The investigated mixed-spin Heisenberg chains can be alternatively viewed as a pure spin-1 Heisenberg chain, which contains at a regular lattice positions spin-2 particles. Unlike the antiferromagnetic spin-1 Heisenberg chain solely displaying a zero magnetization plateau due to the Haldane phase, the ferrimagnetic mixed spin-(1,2), spin-(1,1,2) and spin-(1,1,1,2) Heisenberg chains exhibit more striking magnetization curves involving at least two intermediate magnetization plateaux and quantum spin-liquid states.

Influence of Dzyaloshinskii–Moriya interaction on measurement-induced disturbance in a mixed-spin Heisenberg XXZ model with an inhomogeneous magnetic field

In this paper, by comparing with the thermal entanglement measured by negativity (N), we investigate the measurement-induced disturbance (MID) in a mixed-spin (1/2, 3/2) Heisenberg XXZ model with Dzyaloshinskii–Moriya (DM) interaction and an inhomogeneous external magnetic field. We make a comparison between MID and N, and find that their behaviors present obvious differences following the changes of the exchange constant J, DM interaction D, the uniform magnetic field B and the inhomogeneity of magnetic field b. It is found that J and D broaden the region of MID. At the same time, we notice that, for the case of small D, MID can detect the quantum phase transition near J=0, but not for N. It is also observed that DM interaction and the inhomogeneous external magnetic field play competing roles in enhancing the N and MID in our system. Moreover, we also note D is a more efficient parameter than B and b when adjusting MID under the higher temperature. In addition, we discover that, for the same parameters, the region of MID in our system is larger than the result in mixed-spin (1/2, 1) system.

Green׳s function study of a three-sublattice mixed-spin Heisenberg ferromagnetic and ferrimagnetic system

The magnetic properties of a three-sublattice mixed-spin Heisenberg ferromagnetic and ferrimagnetic system are investigated with the help of the Green׳s function technique in order to clarify some characteristic magnetic behaviors of Prussian-blue compounds. Various types of magnetization curves are obtained, which exhibits one- and two-compensation temperatures. The first-order phase transitions from ferrimagnetic to ferromagnetic state have been observed. There are zero-temperature quantum fluctuations for the ferrimagnet at the absolute state while not for ferromagnet. Moreover, in the case of ferrimagnet, inverted magnetic hysteresis loop with negative coercivity is observed at a certain temperature range and the coercivity takes the value zero at the compensation point.

The multi-compensation temperatures for the four-sublattice Heisenberg ferrimagnetic system

The various types of magnetizations of a four-sublattice mixed-spin Heisenberg ferrimagnetic system are investigated with the help of the double-time temperature-dependent Green’s function technique. One obtains the first-order phase transitions from ferrimagnetic states to ferrimagnetic or ferromagnetic states with respect to the choice of parameters in Hamiltonian. The system exhibits one-, two- and three-compensation temperatures where the sublattice magnetizations compensate each other at one- or more-points. We have managed to obtain three different spin configurations at the absolute temperature. Moreover, we observed a so-called frustrated spin.

Entanglement in a two-spin (1/2, 3/2) mixed-spin Heisenberg XX chain with an inhomogeneous external magnetic field

By using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XX chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature is higher than the results of the spin-1/2 chain and (1/2,1) mixed-spin chain. And by adjusting the nonuniform parameter b, one is able to obtain more entanglement at a higher temperature.

Entanglement in a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field

Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k, and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b, one is able to obtain more entanglement at higher temperature.

The three-dimensional mixed-spin Heisenberg model applied to the magnetic properties of La1−xSrxMnO3 in the random phase approximation

The magnetic properties of the manganese oxide compounds La1−xSrxMnO3 are studied by means of the double-time Green’s function. The phase diagram, magnetization, spin-wave dispersion, and spin-wave stiffness are obtained within the random phase approximation. Our results are in agreement with other theoretical and experimental results.

Implementation of the Fredkin gate with a three-qubit mixed-spin Heisenberg model

We show that a local unitary (LU) equivalent Fredkin gate can be obtained from the free evolution of three mixed-spin qubits by virtue of numerical simulation with only one step. The spin-1 qubit acts as the control qubit, and two spin-1/2 qubits, which interact with the spin-1 qubit via the first neighbor spin interaction, respectively, play the role of target qubits. We also examine the imperfect Fredkin gate operation by considering the effects of nonidentical coupling constants, uniform and inhomogeneous magnetic fields.

Thermal entanglement in a mixed-spin Heisenberg XXZ model under a nonuniform external magnetic field

The thermal entanglement in (1/2,1) mixed-spin Heisenberg XXZ model is investigated under an external nonuniform magnetic field. In the uniform magnetic field system, the critical magnetic field B c and critical temperature T c are increased by increasing the anisotropic parameter k. The degree of magnetic field b plays an important role in improving the critical temperature and enlarging the region of entanglement in the nonuniform magnetic field system.

Monte Carlo study of magnetic properties for the mixed spin-3/2 and spin-1 ferrimagnetic nanoparticles

Based on Monte Carlo simulation, the magnetic properties of the ferrimagnetic nanoparticles on a body-centered-cubic lattice are investigated. The particle is described by a mixed-spin Heisenberg model in which S=3/2 and σ=1 are distributed in the two interpenetrating square sublattices. It is found that no compensation point occurs at finite temperature when only the nearest-neighbor interaction between S–σ spins is included. But, when the next-nearest-neighbor interaction between σ–σ spins is taken into account and exceeds a threshold value that depends on the other parameters such as the next-nearest-neighbor interaction between S–S spins and single-ion anisotropies in the Hamiltonian, a compensation point can appear. With the appropriate order parameter which is constructed to characterize the compensation behavior clearly, a variety of phase diagrams including the finite-size effect are derived and discussed.

Entanglement, purity and fidelity in the anisotropy [formula omitted] mixed-spin system

We study entanglement, purity and fidelity in the anisotropy ( 1 / 2 , 1 ) mixed-spin Heisenberg chain. We find that negativity, as a measure of entanglement, displays a dip at the SU(2) isotropic point of the system, which is in contrast to the peak appearance of concurrence in the spin- 1 / 2 XXZ chain. Moreover, at the isotropic point, purity gives a minimum, while the mixed-state fidelity susceptibility emerges a maximum.

Anisotropy and Magnetic Field Effects on Entanglement of a Two-Spin (1/2,1) Mixed-Spin Heisenberg XY Chain

We study the entanglement in anisotropic (1/2,1) mixed-spin Heisenberg XY model under the presence of an external magnetic field at thermal equilibrium. By adjusting the anisotropic parameter and the magnetic field, one is able to obtain entanglement at higher temperature. We find the evidence of the quantum phase transition in the model and observe that the quantum phase transition point at low temperature moves toward weak magnetic field with the increase of the anisotropic parameter.

Effects of anisotropy and external magnetic field on the thermal entanglement in a (1/2,1) mixed-spin Heisenberg model

In contrast to the spin-half Heisenberg model, we investigate the effects of anisotropy and external magnetic field on thermal entanglement in a (1/2,1) mixed-spin Heisenberg model. By using the concept of negativity, we find the critical temperature Tc and critical magnetic field Bc of mixed-spin are much higher than that of spin-half, and this phenomenon is more evident with increasing anisotropy coefficient Δ. Contrary to the spin-half, we also observe that the nonuniform field can enhance the entanglement of mixed-spin to a great extent.

Entanglement properties in [formula omitted] mixed-spin Heisenberg systems

By using the concept of negativity, we investigate entanglement in ( 1 2 , 1 ) mixed-spin Heisenberg systems. We obtain the analytical results of entanglement in small isotropic Heisenberg clusters with only nearest-neighbor (NN) interactions up to four spins and in the four-spin Heisenberg model with both NN and next-nearest-neighbor (NNN) interactions. For more spins, we numerically study effects of temperature, magnetic fields, and NNN interactions on entanglement. We study in detail the threshold value of the temperature, after which the negativity vanishes.

Phase transition and ferrimagnetic long-range order in the mixed-spin Heisenberg model with single-ion anisotropy

In the present paper, we study the quantum phase transition in the mixed-spin Heisenberg model with the single-ion anisotropy on a bipartite lattice. We prove rigorously that, when the single-ion anisotropy energy $D$ is positive, the model has a unique ground state with the total spin-$z$ component ${S}_{z}=0$. On the other hand, when the single-ion anisotropy energy is negative and favors the longitudinal spin direction, the global ground state of the system becomes doubly degenerate. Therefore, $D=0$ is the bifurcation point for the global ground state of the system. Furthermore, we show also that, in the latter case, the global ground state of the mixed-spin Heisenberg chain has the ferrimagnetic long-range order. Our conclusions confirm and generalize the previous results derived by numerical calculations on small size samples.