A phase diagram of the one-dimensional S=1/2 frustrated ferromagnetic Heisenberg model in a magnetic field is studied via a bosonization technique. Besides the ferromagnetic phase, two different nematiclike phases with additional symmetry breaking of reflections about a bond or about a site are mapped out. The prediction is made of possible fourfold degeneracy of a ground state at H=0 for sufficiently strong second-neighbor coupling.
A phase diagram of the one-dimensional S=1/2 frustrated ferromagnetic Heisenberg model in a magnetic field is studied via a bosonization technique. Besides the ferromagnetic phase, two different nematiclike phases with additional symmetry breaking of reflections about a bond or about a site are mapped out. The prediction is made of possible fourfold degeneracy of a ground state at H=0 for sufficiently strong second-neighbor coupling.
We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor J_2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density matrix renormalization group method and exact diagonalization) and effective field-theory approach, and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J_1/J_2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferro-nematic spin correlation, and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferro-multipolar spin correlations. The multipolar phases cross over to spin density wave phases as the magnetic field is decreased, before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO_4) are discussed.
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 2s 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.
We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J1 and antiferromagnetic next-nearest-neighbor J2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density-matrix renormalization-group method and exact diagonalization) and effective-field-theory approach and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J1/J2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferronematic spin correlation and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferromultipolar spin correlations. The multipolar phases cross over to spin-density-wave phases as the magnetic field is decreased before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO4) are discussed.
We study frustrated spin-1/2 dimer systems in two dimensions with a bilayer structure, where spins are ferromagnetically coupled in dimers. Our model includes frustrated two-spin exchange interactions as well as four-spin interactions. We pay particular attention to the spin nematic phase, which does not exhibit any magnetic (spin-dipole) order but has a spin-quadrupolar long-range order. Employing a perturbation calculation, a mean-field approximation, and a numerical many-variable variational Monte Carlo method, we determine ground-state phase diagrams on various two-dimensional lattices. It is found that the model exhibits the spin nematic phase with ferroquadrupolar order in a wide parameter region, in addition to conventional magnetically ordered phases. In particular, it is shown that even when the four-spin interactions are absent, frustrated two-spin exchange interactions can realize the spin nematic phase as a result of strong interdimer correlations. It is also found that the phase transitions between the spin nematic phase and antiferromagnetic phases can be continuous. Furthermore, we present some exact arguments that various phases including the spin nematic phase and the vector chiral (p-type nematic) phase emerge from an SU(4) symmetric point in the model by the addition of appropriate perturbative interactions. The spin nematic phase generated from the SU(4) point is connected with the spin nematic phase found numerically in the system with only two-spin interactions.
We investigate the quantum spin-1/2 zigzag chain with frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\mathrm{\ensuremath{\Gamma}}$ term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground-state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $\mathrm{\ensuremath{\Gamma}}$ term, we observe the persistent dimer-singlet state of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, sustaining a nonzero spin gap, while also hosting a gapless nonmagnetic excitation that manifests in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode, remaining almost as a fluctuation to the ground state, induces a dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms into the Ising-type ferromagnetic or antiferromagnetic long-range orders. The $\mathrm{\ensuremath{\Gamma}}$ term spontaneously selects magnetic easy axes, and their orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in YbCuS2, characterized by gapless excitations and seemingly nonmagnetic behavior.
The ground-state phase diagram of a spin-21 XXZ chain with competing ferromagnetic nearest-neighbor (J1<0) and antiferromagnetic second-neighbor (J2>0) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.