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 thermodynamics of coupled frustrated ferromagnetic chains is studied within a spin-rotation-invariant Green's-function approach. We consider an isotropic Heisenberg spin-half system with a ferromagnetic in-chain coupling
J1<0 between nearest neighbors and a frustrating antiferromagnetic next-nearest-neighbor in-chain coupling
J2>0. We focus on the moderate strength of frustration
J2<∣J1∣/4 such that the in-chain spin-spin correlations are predominantly ferromagnetic. We consider two interchain couplings (ICs) ${J}_{\ensuremath{\perp},y}$ and ${J}_{\ensuremath{\perp},z}$, corresponding to the two axes perpendicular to the chain, where ferromagnetic as well as antiferromagnetic ICs are taken into account. We discuss the influence of frustration on the ground-state properties for antiferromagnetic ICs, where the ground state is of a quantum nature. The major part of our study is devoted to the finite-temperature properties. We calculate the critical temperature
Tc as a function of the competing exchange couplings ${J}_{2},{J}_{\ensuremath{\perp},y},{J}_{\ensuremath{\perp},z}$. We find that for fixed ICs,
Tc decreases monotonically with increasing frustration
J2, where as ${J}_{2}\ensuremath{\rightarrow}|{J}_{1}|/4$ the
Tc(J2) curve drops down rapidly. To characterize the magnetic ordering below and above
Tc, we calculate the spin-spin correlation functions $\ensuremath{\langle}{\mathbf{S}}_{0}{\mathbf{S}}_{\mathbf{R}}\ensuremath{\rangle}$, the magnetic order parameter
M, the uniform static susceptibility ${\ensuremath{\chi}}_{0}$, as well as the correlation length $\ensuremath{\xi}$. Moreover, we discuss the specific heat
CV and the temperature dependence of the excitation spectrum ${\ensuremath{\omega}}_{\mathbf{q}}$. As ${J}_{2}\ensuremath{\rightarrow}|{J}_{1}|/4$, some unusual frustration-induced features were found, such as an increase of the in-chain spin stiffness (in the case of ferromagnetic ICs) or of the in-chain spin-wave velocity (in the case of antiferromagnetic ICs) with growing temperature.
The thermodynamic properties of a spin
S=1/2 tetrameric Heisenberg antiferromagnetic chain with alternating interactions
AF1-AF2-AF1-F (AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization-group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying
JAF1=JAF2=JF is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility, and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the
S=1 Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.
We study the ground state properties of the Heisenberg spin-
21 chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using two approximate methods. One of them is the Jordan-Wigner mean-field theory and another approach is based on the transformation of spin operators to Bose ones and on the variational treatment of bosonic Hamiltonian. Both approaches give close results for the ground state energy and the magnetization curve at
T=0. It is proved that quantum fluctuations change the classical critical exponents in the vicinity of the transition point from the ferromagnetic to the singlet ground state. The magnetization processes display a different behavior in the regions near and far from the transition point. The relation of the obtained results to the experimental magnetization curve in
Rb2Cu2Mo3O12 is discussed.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(1)(F)) and antiferromagnetic (J(1)(A)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(2)(F)). In this model frustration is present due to the non-zero J(2)(F). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(2)(F) and large J(1)(F)/J(1)(A). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(1)(F), the phase diagram in the space of J(1)(A)-J(2)(F) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (
J1F) and antiferromagnetic (
J1A) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (
J2F). In this model frustration is induced by the non-zero
J2F and the effect of dimerization is realized by changing the strength of
J1A for a fixed value of
J1F. The model with site spin
s behaves like a Haldane spin chain with site spin 2
s in the limit of vanishing
J2F and large
J1F/J1A. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of
J1A−J2F is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.