We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearestneighbor 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 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., LiCuVO4) are discussed.

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We study a one-dimensional Heisenberg chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor interactions in 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 π except for a small parameter range. We argue that bose condensation of the bound n magnons leads to novel Tomonaga-Luttinger liquids with multi-polar correlations; nematic and triatic ordered liquids correspond to n = 2 and n = 3.PACS numbers: 75.10. Jm, 75.10.Pq Frustrated spin chains are simple models that still show surprisingly rich physics. A prototype of these is the spin-1 2 Heisenberg chain with nearest-neighbor (NN) J 1 and next-nearest-neighbor (NNN) J 2 couplings,whereis the spin-1/2 operator on the lth site, and external field h is applied in the z direction. The exchange interactions are frustrated as the NNN interaction is antiferromagnetic (AF), J 2 > 0. Until recently most theoretical studies on the J 1 -J 2 model (1) considered the case where the NN coupling J 1 is also AF. However, interest is now growing rapidly in the ferromagnetic (FM) case (J 1 < 0) as well, which is triggered by experimental reports on thermodynamic properties of various quasi-one-dimensional frustrated FM spin chains (for a list of frustrated quasi-one-dimensional materials, see Table 1 Recent theoretical studies 4,5 have shown that, in a magnetic field, the FM J 1 -J 2 chain (J 1 < 0, J 2 > 0) becomes a Tomonaga-Luttinger (TL) liquid having nematic quasi-long-range order as dominant correlation for some range of J 1 /J 2 . This nematic state can be thought of as arising from condensation of two-magnon bound states. 6 Interestingly, such a nematic ordered phase can also appear in a frustrated FM spin model on the twodimensional square lattice. 7 One can imagine further a bose condensed phase of more-than-two-magnon bound states. Indeed it was shown 8 recently that an octupolarlike triatic ordered phase can result from condensation of three-magnon bound states in a frustrated ferromagnet on the triangular lattice. These results motivated us to examine the possibility of such many-magnon bound states in the FM J 1 -J 2 model (1). In this paper we show, by explicitly constructing bound-state wave functions, that for −3.52 J 1 /J 2 −2.72 the lowest-lying excitations from the fully polarized FM state are 3-magnon bound states, and moreover 4-magnon bound states appear for a slightly stronger FM coupling regime. We then suggest exotic TL liquid phases with multipolar-like spin correlations to emerge from condensation of multimagnon bound states below the saturation field.Before presenting our calculations, let us briefly review known results that are relevant to our study. First, in the classical limit, we may regard S l as a c-number vector of length S. The ground state of (1) in this limit has a (...

The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters $K_{\rho}$ and $v_{\sigma}$. In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density-wave to localized in character as the density is lowered. Our results for $K_{\rho}$ are in good agreement with weak-coupling perturbative estimates $K_{\rho}^{pert}$ at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. $K_{\rho}^{pert}\sim n^{1/2}$ vanishes at small carrier density $n$ whereas we conjecture that $K_{\rho}\to 1/2$ when $n\to 0$, implying that $K_{\rho}$ should pass through a minimum at an intermediate density. Observation of such a non-monotonic dependence on particle density would allow to measure the range of the microscopic interaction. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing $n$. Strong correlation effects make it difficult to obtain fully consistent estimates of $v_{\sigma}$ from Hartree-Fock calculations. We conjecture that $v_{\sigma}/\vf\propto n/V_0$ in the limit $n\to 0$ where $V_0$ is the interaction strength.Comment: RevTeX, 23 pages, 8 figures include