Magnetic properties of zig-zag ladders

Cabra, D. C.; Honecker, A.; Pujol, Pierre

doi:10.1007/s100510050010

Cited by 90 publications

(132 citation statements)

References 67 publications

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“…These nonvanishing averages indicate that the ground state breaks a Z 2 symmetry and has a vector chiral long-range order. Since κ (1) l and κ (2) l have the same sign and satisfy Eq. (6), the spin current J n κ (n) l flows as depicted in Fig.…”

Section: A Bosonization Approach For |J1| ≪ J2mentioning

confidence: 99%

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Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field

et al. 2008

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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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Section: A Bosonization Approach For |J1| ≪ J2mentioning

confidence: 99%

“…The ground state manifold has extensive degeneracy at the phase boundary J 1 /J 2 = −4. 37,38 In magnetic field the spins order with a helical magnetic structure s l /s = (sin θ c cos φ c l , sin θ c sin φ c l , cos θ c ) (2) in the classical limit (s = |s| ≫ 1), with a pitch angle…”

Section: Introductionmentioning

confidence: 99%

Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field

et al. 2008

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“…9 For the parameter range −4J 2 < J 1 < 0 of our main interest, Chubukov 6 suggested that the ground state just below the saturation field should be a nematic state made up of bound magnon pairs with a commensurate total momentum k = π if −2.67J 2 < J 1 < 0 (2.67 ≈ 1/0.38) and with an incommensurate momentum k < π otherwise, which was partly verified by mean-field theory, 10 numerical study, 11 Green's function analysis which fixed the commensurate-incommensurate transition point to J 1 /J 2 = −2.66908 (= −1/0.374661), 12 and weak-coupling bosonization analysis. 4,11,13 While earlier calculations of the ground-state magnetization process suggested metamagnetic transitions, 10,14 recent densitymatrix renormalization group (DMRG) study 11 finds that the total magnetization of finite-size chains changes by ∆S z = 2 at J 1 = −J 2 , ∆S z = 3 at J 1 = −3J 2 , and ∆S z = 4 at J 1 = −3.75J 2 below saturation, implying that the magnetization curve is continuous in the thermodynamic limit. 13 To reveal how the fully polarized FM state collapses into new states with decreasing either magnetic field or the coupling ratio |J 1 |/J 2 , we analyze magnon instability in the fully polarized state.…”

mentioning

confidence: 99%

“…4,11,13 While earlier calculations of the ground-state magnetization process suggested metamagnetic transitions, 10,14 recent densitymatrix renormalization group (DMRG) study 11 finds that the total magnetization of finite-size chains changes by ∆S z = 2 at J 1 = −J 2 , ∆S z = 3 at J 1 = −3J 2 , and ∆S z = 4 at J 1 = −3.75J 2 below saturation, implying that the magnetization curve is continuous in the thermodynamic limit. 13 To reveal how the fully polarized FM state collapses into new states with decreasing either magnetic field or the coupling ratio |J 1 |/J 2 , we analyze magnon instability in the fully polarized state. We apply a large enough magnetic field h such that the fully polarized state is the unique ground state for −4J 2 < J 1 < 0, and all multi-magnon excitations have positive excitation energies which decrease as h is reduced.…”

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confidence: 99%

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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“…It is deserved to mention here that this gap could also survive even for J 1 ≫J 2 ,J 3 , in which the system can be seen as the three free spin chains with intra-chain couplings J 1 perturbed by relevant perturbations generated by the inter-chain couplings J 2 and J 3 , as in the case of spin ladders [24][25][26] . Therefore, this case as well falls into the gapped phase.…”

Section: Bosonization and Low-energy Effective Theorymentioning

confidence: 99%

Low-energy effective theory and two distinct critical phases in a spin-12frustrated three-leg spin tube

et al. 2012

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Motivated by the crystal structures of [(CuCl2tachH)3Cl]Cl2 and Ca3Co2O6, we develop a lowenergy effective theory using the bosonization technique for a spin-1/2 frustrated three-leg spin tube with trigonal prism units in two limit cases. The features obtained with the effective theory are numerically elucidated by the density matrix renormalization group method. Three different quantum phases in the ground state of the system, say, one gapped dimerized phase and two distinct gapless phases, are identified, where the two gapless phases are found to have the conformal central charge c = 1 and 3/2, respectively. Spin gaps, spin and dimer correlation functions, and the entanglement entropy are obtained. In particular, it is disclosed that the critical phase with c = 3/2 is the consequence of spin frustrations, which might belong to SU(2) k=2 Wess-Zumino-WittenNovikov universality class, and is induced by the twist term in the bosonized Hamiltonian density.

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Magnetic properties of zig-zag ladders

Cited by 90 publications

References 67 publications

Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field

Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field

Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

Low-energy effective theory and two distinct critical phases in a spin-12frustrated three-leg spin tube

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