We study the magnetization process of a one-dimensional extended Heisenberg model, the $J\text{\ensuremath{-}}Q$ model, as a function of an external magnetic field
h. In this model,
J represents the traditional antiferromagnetic Heisenberg exchange and
Q is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value ${q}_{c}\ensuremath{\approx}0.85$ where $q\ensuremath{\equiv}Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for
q>qmin, where we have calculated
qmin=92 exactly. For
q>qmin, two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for
q>qmin. Our results show that neither geometric frustration nor spin anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain
(J1>0,J2<0), but only if
J2 is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for $q\ensuremath{\le}{q}_{\mathrm{min}}$ at
T>0. While the expected ``zero-scale-factor'' universality is clearly seen for
q=0 and $q\ensuremath{\ll}{q}_{\mathrm{min}}$, for
q closer to
qmin we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at
qmin. In the low-energy theory, one can expect the quartic nonlinearity to vanish at
qmin and a marginal sixth-order term should govern the scaling, which leads to a crossover at a temperature
T∗(q) between logarithmic tricritical scaling and zero-scale-factor universality, with ${T}^{*}(q)\ensuremath{\rightarrow}0$ when $q\ensuremath{\rightarrow}{q}_{\mathrm{min}}$.
We study a one-dimensional Heisenberg chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions in a magnetic field. Starting from the fully polarized high-field state, we calculate the dispersions of the lowest-lying
n-magnon excitations and the saturation field
(n=2,3,4). We show that the lowest-lying excitations are always bound multimagnon states with a total momentum of $\ensuremath{\pi}$ except for a small parameter range. We argue that Bose condensation of the bound
n magnons leads to novel Tomonaga-Luttinger liquids with multipolar correlations; nematic- and triatic-ordered liquids correspond to
n=2 and
n=3.
We study few-magnon excitations in a finite-size spin-
S chain with ferromagnetic nearest-neighbor (NN) interaction
J>0 and antiferromagnetic next-nearest-neighbor (NNN) interaction ${J}^{\ensuremath{'}}<0$, in the presence of the single-ion (SI) anisotropy
D. We first reveal the condition for the emergence of zero-excitation-energy states. In the isotropic case with $\mathrm{\ensuremath{\Delta}}={\mathrm{\ensuremath{\Delta}}}^{\ensuremath{'}}=1$ ($\mathrm{\ensuremath{\Delta}}$ and ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{'}}$ are the corresponding anisotropy parameters), a threshold of $J/|{J}^{\ensuremath{'}}|$, above which the ground state is ferromagnetic, is determined by exact diagonalization for short chains up to 12 sites. Using a set of exact two-magnon Bloch states, we then map the two-magnon problem to a single-particle one on an effective open chain with both NN and NNN hoppings. The whole two-magnon excitation spectrum is calculated for large systems, and the commensurate-incommensurate transition in the lowest-lying mode is found to exhibit different behaviors between
S=1/2 and higher spins due to the interplay of the SI anisotropy and the NNN interaction. For the commensurate momentum $k=\ensuremath{-}\ensuremath{\pi}$, the effective lattice is decoupled into two NN open chains that can be exactly solved via a plane-wave ansatz. Based on this, we analytically identify in the ${\mathrm{\ensuremath{\Delta}}}^{\ensuremath{'}}\ensuremath{-}D/|{J}^{\ensuremath{'}}|$ plane the regions supporting the SI or NNN exchange two-magnon bound states near the edge of the band. In particular, we prove that there always exists a lower-lying NN exchange two-magnon bound state near the band edge for arbitrary $S\ensuremath{\ge}1/2$. Finally, we numerically calculate the
n-magnon spectra for
S=1/2 with $n\ensuremath{\le}5$ by using a spin-operator matrix element method. The corresponding
n-magnon commensurate instability regions are determined for finite chains, and consistent results with prior literature are observed.
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.
Abstract We investigate magnetic excitations and spin transport properties of a frustrated spin chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in a magnetic field by density-matrix renormalization group methods. In the field-induced quadrupole and octupole regimes, the low-energy excitation is governed by two-and three-magnon bound states, respectively, so that bound magnon clusters would contribute to the spin transport. We show that spin current correlations decrease when the system goes from the quadrupole regime into the octupole regime. This indicates that the spin transport is suppressed in the octupole regime, although bound three-magnon clusters carry a larger amount of angular momentum than bound two-magnon clusters.
We study the magnetic field-dependence of the thermal conductivity due to magnetic excitations in frustrated spin-1/2 Heisenberg chains. Near the saturation field, the system is described by a dilute gas of weakly interacting fermions (free-fermion fixed point). We show that in this regime the thermal conductivity exhibits a nonmonotonic behavior as a function of the ratio $\ensuremath{\alpha}={J}_{2}/{J}_{1}$ between second- and first-nearest-neighbor antiferromagnetic exchange interactions. This result is a direct consequence of the splitting of the single-particle dispersion minimum into two minima that takes place at the Lifshitz point $\ensuremath{\alpha}=1/4$. Upon increasing $\ensuremath{\alpha}$ from zero, the inverse mass vanishes at $\ensuremath{\alpha}=1/4$ and it increases monotonically from zero for $\ensuremath{\alpha}\ensuremath{\ge}1/4$. By deriving an effective low-energy theory of the dilute gas of fermions, we demonstrate that the Drude weight
Kth of the thermal conductivity exhibits a similar dependence on $\ensuremath{\alpha}$ near the saturation field. Moreover, this theory predicts a transition between a two-component Tomonaga-Luttinger liquid and a vector-chiral phase at a critical value $\ensuremath{\alpha}={\ensuremath{\alpha}}_{c}$ that agrees very well with previous density matrix renormalization group results. We also show that the resulting curve ${K}_{\mathrm{th}}(\ensuremath{\alpha})$ is in excellent agreement with exact diagonalization (ED) results. For the low-magnetic field regime, our ED results show that ${K}_{\mathrm{th}}(\ensuremath{\alpha})$ has a pronounced minimum at $\ensuremath{\alpha}\ensuremath{\simeq}0.7$. We also demonstrate that the thermal conductivity is significantly affected by the presence of magnetothermal coupling.