The elementary excitation spectra of the one-dimensional spin-1/2 XY model in the ferrimagnetic diamond chain at low temperature are calculated by using invariant eigenvector in this paper. And the elementary excitation energies in different cases are discussed. Therefore, analytic solutions of the three critical magnetic field intensities HC1, HC2 and Hpeak in the system are given. It is found that the analytic solutions of three critical magnetic field intensities are correct from the law of the magnetization changing with temperature under different external magnetic fields, and it is explained by the contributions of the three elementary excitations to the magnetization. The external magnetic field dependent magnetization presents a 1/3 magnetized plateau at low temperature. The variation of magnetic susceptibility either with temperature or with external magnetic field shows a double peak structure, this phenomenon indicates that the double peak structure originates from the competition among the ferromagnetic exchange interaction energy of intramolecular electronic spin parallel arrangement in dimer, the antiferromagnetic exchange interaction energy of intermolecular electronic spin antiparallel arrangement in dimer-monomer, the thermal disorder energy and the spin magnetic moment potential energy related to external magnetic field.
The elementary excitation spectra of the one-dimensional spin-1/2 XY model in the ferrimagnetic diamond chain at low temperature are calculated by using invariant eigenvector in this paper. And the elementary excitation energies in different cases are discussed. Therefore, analytic solutions of the three critical magnetic field intensities HC1, HC2 and Hpeak in the system are given. It is found that the analytic solutions of three critical magnetic field intensities are correct from the law of the magnetization changing with temperature under different external magnetic fields, and it is explained by the contributions of the three elementary excitations to the magnetization. The external magnetic field dependent magnetization presents a 1/3 magnetized plateau at low temperature. The variation of magnetic susceptibility either with temperature or with external magnetic field shows a double peak structure, this phenomenon indicates that the double peak structure originates from the competition among the ferromagnetic exchange interaction energy of intramolecular electronic spin parallel arrangement in dimer, the antiferromagnetic exchange interaction energy of intermolecular electronic spin antiparallel arrangement in dimer-monomer, the thermal disorder energy and the spin magnetic moment potential energy related to external magnetic field.
We used the Jordan–Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H CB, H CE and H CS were obtained, in which the H CB and H CE correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H CS correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ℏ ω σ,k (σ = 1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., [ℏ ω 3,k (H CB)]min = 0, [ℏ ω 2,k (H CE)]max = 0 and [ℏ ω 2,k (H CS)]min = 0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system’s magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the 1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.
We investigate the ground state properties, magnetization, and low-temperature thermodynamics of the ferromagnetic-antiferromagnetic spin-s model on diamond-decorated lattices with ideal diamond units, incorporating bilinear Heisenberg and higher-order exchange interactions between diagonal spins-σ. Local conservation of the composite spin on each diamond diagonal enables exact analysis. For the pure Heisenberg case, the system undergoes a series of 2σ transitions between monomer-dimer (MD), ferrimagnetic (Ferri) and ferromagnetic (F) phases with different optimal composite spin values as the coupling ratio varies. In the presence of higher-order interactions, a multicritical point exists where the states with all possible values of composite spin are degenerate, leading to maximal ground state degeneracy. The case s=σ=1 with bilinear and biquadratic interactions is studied in detail. Its phase diagram comprises three phases - F, Ferri and MD, which meet at a triple point. On the phase boundaries, the ground state becomes macroscopically degenerate. For the diamond chain, we calculate the ground state degeneracy exactly; for higher dimensions, the problem maps onto a bond percolation framework, solved numerically. The residual entropy per spin reaches up to 60% of the maximal value, peaking at the triple point. Low-temperature magnetization curves in external magnetic fields exhibit plateaus and jumps. The excitation spectrum is gapped in the MD phase, gapless in the F phase, and resembles that of the Lieb-Mattis ferrimagnet in the Ferri phase. The high residual entropy suggests potential applications in ultra-low-temperature cooling and quantum thermal machines.
The low-dimensional quantum spin systems have been extensively studied in the past three decades due to the novel ground states and rich magnetic behaviors,especially the quantum spin chain with diamond topology structure. Motivated by recent experimental success in Cu3(CO3)2(OH)2 compound,which is regarded as a model material of spin-1/2 diamond chain,researchers have paid a lot of attention to various variants of diamond spin chains.In this paper,we mainly examine the magnetic properties of an antisymmetric spin-1/2 Ising-Heisenberg diamond chain with the secondneighbor interaction between nodal spins.By using exact diagonalization and transfer-matrix methods,the ground-state phase diagram,magnetization behavior and macroscopic thermodynamics are exactly solved for the particular case that all magnetic bonds yield antiferromagnetic couplings,which usually shows the most interesting magnetic features closely related to a striking interplay between geometric frustration and quantum fluctuations.To clearly illustrate the effect of second-neighbor interaction item,we consider a highly frustrated situation that all Ising-Heisenberg bonds and Heisenberg bonds possess the same interaction strength.The calculation results indicate that the second-neighbor interaction item will enrich ground states and magnetization plateaus.A classical ferrimagnetic phase FRI1 corresponding to a novel two-thirds of intermediate plateau with translationally broken symmetry is introduced,manifesting itself as up-up-up-down-up-up spin configuration at a ground-state.In addition,there are other four distinct ground states which can be identified from the phase diagram,i.e.,one saturated paramagnetic phase SP,one classical ferrimagnetic phase FRI2,one quantum ferrimagnetic phase QFI and the unique quantum antiferromagnetic phase QAF.The classical phase FRI2 and quantum phase QFI both generate one-third of magnetization plateau.It is worth mentioning that all the values of these magnetization plateaus satisfy the Oshikawa-Yamanaka-Affleck condition.Besides,the results also have shown a rich variety of temperature dependence of total magnetization and specific heat.The magnetization displays the remarkable thermal-induced changes as the external field is sufficiently close to critical value where two or more than two different ground states coexist.At the critical field relevant to a coexistence of two different states,the total magnetization displays a monotonic decrease trend.The thermal dependence of zero-field specific heat displays relative complex variations for different second-neighbor interactions between nodal spins.At first,the specific heat presents only a single rounded Schottky-type maximum.Using the second-neighbor interaction,another sharp peak arises at low-temperature and is superimposed on this round maximum,and the specific heat exhibits a double-peak structure. On further strengthening,the low-temperature one keeps its height shifting towards high temperature,while the hightemperature round peak suffers great enhancement and moves in an opposite direction.Finally,the low temperature peak entirely merges with the Schottky-type peak at a certain value of second-neighbor interaction,and above this value, the specific curve recovers its single peak structure.The observed double-peak specific heat curves mainly originate from thermal excitations between the ground-state spin configuration QAF and the ones close enough in energy to the ground state.
The magnetic and thermodynamic properties of spin-1∕2 Heisenberg diamond chains are investigated in three different cases: (a) J1, J2, J3>0 (frustrated), (b) J1, J3<0, J2>0 (frustrated), and (c) J1, J2>0, J3<0 (nonfrustrated), where the bond coupling Ji(i=1,2,3)>0 stands for an antiferromagnetic (AF) interaction, and <0 for a ferromagnetic (F) interaction. The density-matrix renormalization-group (DMRG) technique is invoked to study the properties of the system in the ground state, while the transfer-matrix renormalization-group (TMRG) technique is applied to explore the thermodynamic properties. The local magnetic moments, spin-correlation functions, and static structure factors are discussed in the ground state for the three cases. It is shown that the static structure factor S(q) shows peaks at wave vectors $q=a\ensuremath{\pi}∕3$ (a=0,1,2,3,4,5) for different couplings in a zero magnetic field, which, however, in the magnetic fields where the magnetization plateau with m=1∕6 pertains, exhibits the peaks only at q=0, $2\ensuremath{\pi}∕3$, and $4\ensuremath{\pi}∕3$, which are found to be couplings independent. The DMRG results of the zero-field static structure factor can be nicely fitted by a linear superposition of six modes, where two fitting equations are proposed. It is observed that the six modes are closely related to the low-lying excitations of the system. At finite temperatures, the magnetization, susceptibility, and specific heat show various behaviors for different couplings. The double-peak structures of the susceptibility, and specific heat against temperature are obtained, where the peak positions and heights are found to depend on the competition of the couplings. It is also uncovered that the XXZ anisotropy of F and AF couplings leads the system of case (c) to display quite different behaviors. In addition, the experimental data of the susceptibility, specific heat, and magnetization for the compound Cu3(CO3)2(OH)2 are fairly compared with our TMRG results.
The thermodynamic properties of the spin-1/2 diamond quantum Heisenberg chain model have been investigated by means of the transfer matrix renormalization group (TMRG) method. Considering different crystal structures, by changing the interactions among different spins and the external magnetic fields, we first investigate the magnetic susceptibility, magnetization, and specific heat of the distorted diamond chain as a model of ferrimagnetic spin systems. The susceptibility and the specific heat show different features for different ferromagnetic (F) and antiferromagnetic (AF) interactions and different magnetic fields. A 1/3 magnetization plateau is observed at low temperature in a magnetization curve. Then, we discuss the theoretical mechanism of the double-peak structure of the magnetic susceptibility and the three-peak structure of the specific heat of the compound Cu3(CO3)2(OH)2, on which an elegant measurement was performed by Kikuchi et al. [Phys. Rev. Lett. 94, 227201 (2005)]. Our computed results are consistent with the main characteristics of the experimental data. Meanwhile, we find that the double-peak structure of susceptibility can be found in several different kinds of spin interactions in the diamond chain. Moreover, a three-peak behavior is observed in the TMRG results of magnetic susceptibility. In addition, we perform calculations relevant for some experiments and explain the characteristics of these materials.
The exact solution of the distorted Ising-Hubbard model for a diamond chain is obtained by means of transfer matrix method. Based on this solution the magnetic, thermal and concurrence properties of the system are studied. We discuss in detail the ground state varying values of Ising and Hubbard interaction couplings, hopping amplitude, magnetic field, chemical potential and get paramagnetic, ferromagnetic, antiferromagnetic and ferrimagnetic phases of the system. Plateaus in magnetization curves and several-peak structures of the specific heat curve for different values of Hamiltonian parameters are obtained. The dependence of concurrence in Hubbard dimers from chain parameters, external magnetic field and temperature are studied.