Frustrated ferromagnetic spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:math>chain in a magnetic field

Дмитриев, Д. В.; Krivnov, V. Ya.

doi:10.1103/physrevb.73.024402

Cited by 62 publications

(86 citation statements)

References 24 publications

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“…However, as shown by earlier studies, 4,6,10,11,12 this is not the true instability for the quantum case in the whole parameter region −4J 2 < J 1 < 0.…”

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confidence: 84%

Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

2007

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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 (...

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“…However, as shown by earlier studies, 4,6,10,11,12 this is not the true instability for the quantum case in the whole parameter region −4J 2 < J 1 < 0.…”

mentioning

confidence: 84%

Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

2007

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“…The isotropic case of this model (∆ 1 = ∆ 2 = 1) is intensively studied last years [11,12,21,22,23]. It is known that the ground state of the isotropic version of the model (1) is ferromagnetic at 0 < J < 1/4 and it becomes a singlet incommensurate state for J > 1/4 [24,25].…”

Section: Introductionmentioning

confidence: 99%

Weakly anisotropic frustrated zigzag spin chain

Дмитриев

Krivnov

2008

Phys. Rev. B

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The frustrated spin-1/2 model with weakly anisotropic ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchanges is studied with use of variational mean-field approach, scaling estimates of the infrared divergencies in the perturbation theory and finite-size calculations. The ground state phase diagram of this model contains three phases: the ferromagnetic phase, the commensurate spin-liquid phase and the incommensurate phase. The non-trivial behavior of the boundaries between these phases and the character of the phase transitions in case of weak anisotropy are determined.

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“…More recently, this model has attracted a fresh surge of theoretical attention [20,32,33,34,35,36,37,38,39], partly due to the appearance of materials whose spin physics is described by this model (see references in [20,32]). Most studies concentrate on finite magnetic fields or finite temperatures and on properties in the thermodynamic limit [20,28,29,30,31,32,33,34,35,36,37,38], or very near the transition point atβ = 4 [27,34,39,40].…”

Section: Frustrated Ferromagnetic Ringsmentioning

confidence: 99%

Entanglement and level crossings in frustrated ferromagnetic rings

2009

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We study the entanglement content of a class of mesoscopic tunable magnetic systems. The systems are closed finite spin-1/2 chains with ferromagnetic nearest-neighbor interactions frustrated by antiferromagnetic next-nearest-neighbor interactions. The finite chains display a series of level crossings reflecting the incommensurate physics of the corresponding infinite-size chain. We present dramatic entanglement signatures characterizing these unusual level crossings. We focus on multispin and global measures of entanglement rather than only one-spin or two-spin entanglements. We compare and contrast the information obtained from these measures to that obtained from traditional condensed matter measures such as correlation functions.

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Frustrated ferromagnetic spin-12chain in a magnetic field

Cited by 62 publications

References 24 publications

Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

Weakly anisotropic frustrated zigzag spin chain

Entanglement and level crossings in frustrated ferromagnetic rings

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