We study the spin-
21 antiferromagnetic Heisenberg chain in both uniform and (perpendicular) staggered magnetic fields using the density-matrix renormalization-group method. This model has been shown earlier to describe the physics of the copper benzoate materials in magnetic field. In the present work, we extend the study to more general case for a systematic investigation of the field-induced gap and related properties of the spin-
21 antiferromagnetic Heisenberg chain. In particular, we explore the high magnetic field regime where interesting behaviors in the field-induced gap, magnetization, and spin correlation functions are found. Careful examination of the low energy properties and magnetization reveals interesting competing effects of the staggered and uniform fields. The incommensurate behavior in the spin correlation functions is demonstrated and discussed in detail. The present work reproduces earlier results in good agreement with experimental data on copper benzoate and predicts new interesting field-induced features at very high magnetic field.
This article is a review of the recent achievements in experimental studies of magnetic excitations in the copper pyrimidine dinitrate [PM–Cu(NO3)2(H2O)2]n (PM = pyrimidine), an S = 1/2 antiferromagnetic chain material with an alternating g-tensor and the Dzyaloshinskii–Moriya interaction, by means of high-field electron spin resonance (ESR). Due to this alternation, in the 1D critical regime this material exhibits a field-induced gap. The excitation spectrum is formed by solitons and their bound states, breathers, and can be effectively described using the sine-Gordon model. With increasing temperature, the soliton-breather regime can be suppressed, resulting in a substantial evolution of ESR parameters. These changes can be described using a new theoretical concept recently proposed for S = 1/2 AF chains with a staggered transverse field. High magnetic field induces a transition into the spin-polarized state with the excitation spectrum formed by magnons. Nonmonotonous behavior of the field-induced gap is observed in vicinity of the saturation field. Experimental data are compared with results of existing theoretical approaches, revealing excellent agreement with predictions.
Using the density-matrix-renormalization-group technique, we calculate numerically the low-energy excitation spectrum and magnetization curve of the spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected to describe the physics of the ${R}_{2}{\mathrm{BaNiO}}_{5} (R\ensuremath{\ne}Y)$ family below the N\'eel temperature of the magnetic rare-earth (R) sublattice. These results are valid in the entire range of the staggered field, and agree with those given by the nonlinear $\ensuremath{\sigma}$ model study for small fields, but differ from the latter for large fields. They are consistent with the available experimental data. The correlation functions for this model are also calculated. The transverse correlations display the anticipated exponential decay with shorter correlation length, while the longitudinal correlations show explicitly the induced staggered magnetization.
We measured the magnetization processes of the S = 1/2 antiferromagnetic chain compound, Cu benzoate. From the inelastic neutron scattering and the specific heat measurements it was recently discovered that the substance exhibits an unexpected gap which varies approximately as the 2/3 power of an applied magnetic field. The primary mechanism of the gap formation is produced by an effective staggered field due to both the alternating g-tensor and the Dzyaloshinskii-Moriya interaction. We observed the effect of the effective staggered field on the magnetization process of Cu benzoate as a rounding behavior near the saturation field as well as an initial nonlinear increment near zero field. The experimental results are well reproduced by the numerical calculation on the Hamiltonian which includes the appropriate term of the staggered field, using the finite temperature density matrix renormalization group method.
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.
Quasi-one-dimensional magnetic materials provide important test beds for rigorous models of interacting many-body systems. Nevertheless, there have been few studies of finite temperature effects on spin correlations in low-spin systems, though these are most likely to exhibit quantum effects. Copper benzoate, Cu(C6D5COO)2⋅3D2O, is a good realization of the S=1/2 Heisenberg antiferromagnetic chain (HAFC). We have performed ac susceptibility and inelastic neutron scattering experiments on this material which establish the Hamiltonian and an excitation spectrum which is consistent with the spinon continuum ansatz of Müller et al. We present inelastic neutron scattering measurements of the temperature evolution of the dynamic spin–spin correlation function Szz(π,ω). Comparison will be made to the classical prediction and to a finite temperature field theory of Schulz as applied to this S=1/2 HAFC.