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We study the one-dimensional spin-1/2 Heisenberg chain with competingferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighborJ_2 exchange couplings in the presence of magnetic field. We use both numericalapproaches (the density matrix renormalization group method and exactdiagonalization) and effective field-theory approach, and obtain theground-state phase diagram for wide parameter range of the coupling ratioJ_1/J_2. The phase diagram is rich and has a variety of phases, including thevector chiral phase, the nematic phase, and other multipolar phases. In thevector chiral phase, which appears in relatively weak magnetic field, theground state exhibits long-range order (LRO) of vector chirality whichspontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO ofantiferro-nematic spin correlation, and arises as a result of formation oftwo-magnon bound states in high magnetic fields. Similarly, the highermultipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formedthrough binding of p magnons near the saturation fields, showing quasi-LRO ofantiferro-multipolar spin correlations. The multipolar phases cross over tospin density wave phases as the magnetic field is decreased, beforeencountering 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.

Vector chiral and multipolar orders in the spin-1/2 frustrated ferromagnetic chain in magnetic field