Heisenberg Diamond Chain Research Articles

Frustrated magnetism of spin- 12 Heisenberg diamond and octahedral chains as a statistical mechanical monomer-dimer problem

It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-$\frac{1}{2}$ Heisenberg diamond and octahedral chains. In addition to monomeric particles assigned within the localized-magnon theory to bound one- and two-magnon eigenstates, the effective monomer-dimer lattice-gas model includes dimeric particles assigned to a singlet-tetramer (singlet-hexamer) state as a cornerstone of dimer-tetramer (tetramer-hexamer) ground state of a spin-$\frac{1}{2}$ Heisenberg diamond (octahedral) chain. The feasibility of the effective description is confirmed through the exact diagonalization and finite-temperature Lanczos methods. Both quantum spin chains display rich ground-state phase diagrams including discontinuous as well as continuous field-driven phase transitions, whereby the specific heat shows in vicinity of the former phase transitions an extraordinary low-temperature peak coming from a highly degenerate manifold of low-lying excitations.

Spotlighting quantum phase transition in spin -1/2 Ising–Heisenberg diamond chain employing Measurement-Induced Nonlocality

We examine thermal quantum correlations characterized by Measurement-Induced Nonlocality (MIN) in an infinite spin-1/2 Ising–Heisenberg spin chain with Dzyaloshinskii–Moriya (DM) interaction. We evaluate MIN analytically in the thermodynamic limit using the transfer matrix approach and show that the MIN and its first-order derivative may spotlight the quantum criticality and quantum phase transition (QPT). We observe that the DM interaction reduces the role of anisotropy parameter in initiating QPT. Further, the DM interaction also induces the nonlocality in the system if the spins are unentangled and greatly enhances the quantum correlations if the spins are correlated. The impact of the magnetic field and temperature on quantum correlations is also brought out at a critical point.

Thermal quantum correlations of a spin-1/2 Ising–Heisenberg diamond chain with Dzyaloshinskii–Moriya interaction**Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).

We investigate the properties of thermal quantum correlations in an infinite spin-1/2 Ising–Heisenberg diamond chain with Dzyaloshinskii–Moriya (DM) interaction. The thermal quantum discord (TQD) and the thermal entanglement (TE) are discussed as two kinds of important methods to measure the quantum correlation, respectively. It is found that DM interaction plays an important role in the thermal quantum correlations of the system. It can enhance the thermal quantum correlations by increasing DM interaction. Furthermore, the thermal quantum correlations can be promoted by tuning the external magnetic field and the Heisenberg coupling parameter in the antiferromagnetic system. It is shown that the behaviors of TQD differ from those of TE. TQD is more robust against decoherence than TE. For the measurement of TQD, the “regrowth” phenomenon occurs in the ferromagnetic system. We also find that the anisotropy favors the thermal quantum correlations of the system with weak DM interaction.

Thermal entanglement of the spin-1 Ising–Heisenberg diamond chain with biquadratic interaction**Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).

We investigate the thermal entanglement of the spin-1 Ising–Heisenberg diamond chain, which can be regarded as a theoretical model for the homometallic molecular ferrimagnet . Two cases, i.e., the isotropic Heisenberg (Ising–XXX) coupling model and anisotropic Heisenberg (Ising–XXZ) coupling model, are discussed respectively. The negativity is chosen as the measurement of the thermal entanglement. By means of the transfer-matrix approach, we focus on the effects of biquadratic interaction parameters on the negativity of the infinite spin-1 Ising–Heisenberg diamond chain. In the Ising–XXX coupling model, it is shown that for the case with ferromagnetic coupling the thermal entanglement can be induced by the biquadratic interaction, but the external magnetic field will suppress the occurrence of the entanglement induced by the biquadratic interaction. In the Ising–XXZ coupling model, for the case with antiferromagnetic coupling, due to the biquadratic interaction the effect of the anisotropy parameter on the entanglement will be suppressed at near-zero temperature. Moreover, the biquadratic interaction makes the threshold temperature increase. The effects of the external magnetic field on the thermal entanglement are also discussed, and it is observed that the entanglement revival phenomena exist in both models considered.

Exactly solvable spin-1 Ising–Heisenberg diamond chain with the second-neighbor interaction between nodal spins

The spin-1 Ising–Heisenberg diamond chain with the second-neighbor interaction between nodal spins is rigorously solved using the transfer-matrix method. In particular, exact results for the ground state, magnetization process and specific heat are presented and discussed. It is shown that further-neighbor interaction between nodal spins gives rise to three novel ground states with a translationally broken symmetry, but at the same time, does not increases the total number of intermediate plateaus in a zero-temperature magnetization curve compared with the simplified model without this interaction term. The zero-field specific heat displays interesting thermal dependencies with a single- or double-peak structure.

Thermal entanglement of the Ising–Heisenberg diamond chain with Dzyaloshinskii–Moriya interaction**Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).

We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction contributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including Dz and Dx, on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters (Dz and Dx) have remarkably different influences on the entanglement. Different from the case Dz, there is the non-monotonic variation of the concurrence with temperature in the case Dx, and additionally the DM interaction Dx can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case Dx is larger than that of the case Dz.

Entanglement, magnetic and quadrupole moments properties of the mixed spin Ising–Heisenberg diamond chain

Thermal entanglement, magnetic and quadrupole moments properties of the mixed spin-12 and spin-1 Ising–Heisenberg model on a diamond chain are considered. Magnetization and quadrupole moment plateaus are observed for the antiferromagnetic couplings. Thermal negativity as a measure of quantum entanglement of the mixed spin system is calculated. Different behavior for the negativity is obtained for the various values of Heisenberg dipolar and quadrupole couplings. The intermediate plateau of the negativity has been observed at the absence of the single-ion anisotropy and quadrupole interaction term. When dipolar and quadrupole couplings are equal there is a similar behavior of negativity and quadrupole moment.

Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy

Abstract The mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy is exactly solved through the generalized decoration–iteration transformation and the transfer-matrix method. The decoration–iteration transformation is first used for establishing a rigorous mapping equivalence with the corresponding spin-1 Blume–Emery–Griffiths chain, which is subsequently exactly treated within the transfer-matrix technique. Apart from three classical ground states the model exhibits three striking quantum ground states in which a singlet-dimer state of the interstitial Heisenberg spins is accompanied either with a frustrated state or a polarized state or a non-magnetic state of the nodal Ising spins. It is evidenced that two magnetization plateaus at zero and/or one-half of the saturation magnetization may appear in low-temperature magnetization curves. The specific heat may display remarkable temperature dependences with up to three and four distinct round maxima in a zero and non-zero magnetic field, respectively.

Magnetization plateaus of an exactly solvable spin-1 Ising–Heisenberg diamond chain

The spin-1 Ising–Heisenberg diamond chain in a magnetic field is exactly solved by a rigorous treatment based on the transfer-matrix method. An exact ground-state phase diagram includes in total three unconventional quantum ground states with a quantum entanglement of the decorating spin-1 Heisenberg dimers apart from two ground states with a classical spin arrangement. It is evidenced that all three values of the magnetization allowed for the spin-1 diamond chain without translationally broken symmetry by the Oshikawa–Yamanaka–Affleck criterion can become evident in an outstanding stepwise magnetization curve with three intermediate plateaus at zero, one-third, and two-thirds of the saturation magnetization.

Magnetocaloric effect in an Ising–Heisenberg diamond chain with direct monomer spin couplings

We study the magnetocaloric effect (MCE) in a spin’ distorted Ising–Heisenberg diamond chain with direct monomer spin couplings. The ground state, isoentropy curves, and adiabatic cooling rate are examined within an exact analytical approach based on the transfer‐matrix technique. We find that the enhancing MCE in the vicinity of the critical field is very sensitive to the nature of field‐induced phase transitions. When the ground‐state phase transitions result from breaking up quantum entanglement states of Heisenberg spins, close to these critical fields, the signal associated with the cooling rate is very small and strongly suppressed by thermal fluctuations. By contrast, the one near the saturation field corresponding to the destruction of antiferromagnetic Ising spin order is considerably large and presents a complex temperature dependence. Interestingly, it can even be enhanced by temperature; this property reflects the intrinsic properties of the antiferromagnetic Ising spin chain and favors the use of frustrated antiferromagnets as promising working substances in low‐temperature magnetic refrigeration.

Exact results for a generalized spin‐1/2 Ising–Heisenberg diamond chain with the second‐neighbor interaction between nodal spins

The ground state and thermodynamics of a generalized spin‐1/2 Ising–Heisenberg diamond chain with the second‐neighbor interaction between nodal spins are calculated exactly using the mapping method based on the decoration–iteration transformation. Rigorous results for the magnetization, susceptibility, and heat capacity are investigated in dependence on temperature and magnetic field for the frustrated diamond spin chain with the antiferromagnetic Ising and Heisenberg interactions. It is demonstrated that the second‐neighbor interaction between nodal spins gives rise to a greater diversity of low‐temperature magnetization curves, which may include an intermediate plateau at two‐third of the saturation magnetization related to the classical ferrimagnetic (up–up–up–down–up–up–) ground state with translationally broken symmetry besides an intermediate one‐third magnetization plateau reflecting the translationally invariant quantum ferrimagnetic (monomer–dimer) spin arrangement.

Magnetic properties of the spin‐1/2 Ising–Heisenberg diamond chain with the four‐spin interaction

AbstractA symmetric spin‐1/2 Ising–Heisenberg diamond chain with the Ising four‐spin interaction is exactly solved by means of the generalized decoration‐iteration mapping transformation. The ground state, the magnetization process and thermodynamics are particularly examined for the case of antiferromagnetic pair interactions (Ising and isotropic Heisenberg ones). It is shown that an interplay between pair interactions, the four‐spin interaction and the external magnetic field gives rise to several quantum ground states with entangled spin states in addition to some semi‐classically ordered ones. Besides, the temperature dependence of the magnetic susceptibility multiplied by the temperature is studied and the interesting triple‐peak specific heat curve is also detected when considering the zero‐field region rather close to the triple point, where three different ground states coexist.

Diamond chains with multiple-spin exchange interactions

We study the phase diagram of a symmetric spin-1/2 Heisenberg diamond chain with additional cyclic four-spin exchange interactions. The presented analysis supplemented by numerical exact-diagonalization results for finite periodic clusters implies a rich phase diagram containing, apart from standard magnetic and spin-liquid phases, two different tetramer-dimer phases as well as an exotic fourfold degenerate dimerized phase. The characteristics of the established spin phases as well as the nature of quantum phase transitions are discussed as well.

Spin frustration in an exactly solvable Ising?Heisenberg diamond chain*1

Exact results of a mixed spin-12 and spin-1 Ising–Heisenberg diamond chain are obtained applying a generalized decoration–iteration transformation. Depending on the values of external field, exchange parameters and anisotropy there exist six different phases in the ground state of the system. The magnetic order of these phases is briefly described in this work.

Spin frustration in an exactly solvable Ising–Heisenberg diamond chain

Exact results of a mixed spin-1/2 and spin-1 Ising-Heisenberg diamond chain are obtained applying a generalized decoration-iteration transformation. Depending on the values of external field, exchange parameters and anisotropy, there exist six different phases in the ground state of the system. The magnetic order of these phases is briefly described in this work.