Static and dynamic structure factors in the Haldane phase of the bilinear-biquadratic spin-1 chain

Schmitt, Andreas; Mütter, K.-H.; Karbach, Michael; Yu, Yongmin; Müller, Gerhard

doi:10.1103/physrevb.58.5498

Cited by 30 publications

(53 citation statements)

References 32 publications

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“…The period 3 phase -The existence of an extended critical phase with soft modes at k = ±2π/3 has first been reported in [18] and further analyzed and interpreted in [19,20,21]. Our results presented in the first part raise the question whether this critical region is of spin nematic character as well.…”

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confidence: 59%

Spin nematics correlations in bilinear-biquadraticS=1spin chains

Läuchli¹,

2006

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We report the existence of an extended critical, nondimerized region in the phase diagram of the bilinear-biquadratic spin-one chain. The dominant power law correlations are ferroquadrupolar i.e. spin nematic in character. Another known critical region is also characterized by dominant quadrupolar correlations, although with a different wave vector. Our results show that spin nematic correlations play an important role in quantum magnets with spin S ≥ 1 in regions between antiferromagnetic and ferromagnetic phases.PACS numbers: 75.10. Jm, 75.10.Pq, 75.40.Mg, 75.40.Cx The recent experimental demonstration [1] of the transition to a Mott insulating state of atoms in an optical lattice from a superfluid state has opened the way to novel realizations of effective quantum lattice models with widely tunable control parameters. Quantum magnetic systems can be realized by spinor atoms in an optical lattice, e.g.23 Na with a total S = 1 moment. Confining S = 1 atoms to an optical lattice there are two scattering channels for identical atoms with total spin S = 0, 2 which can be mapped to an effective bilinear and biquadratic spin interaction [2,3]:where we adopt the standard parametrization J = cos θ and J q = sin θ. In one dimension, the bilinearbiquadratic spin-one model has a rich phase diagram (see Fig. 1 In dimensions higher than one, the bilinear-biquadratic spin-one model is well understood in the relevant parameter regime. It exhibits a spin nematic phase with a finite spin quadrupole moment in the groundstate [10,11].In this Letter we propose a novel scenario for the phase diagram of the one-dimensional model in between the dimerized and the ferromagnetic phases. In particular, we substantiate the existence of an extended critical, nondimerized region with dominant spin nematic correlations using extensive numerical simulations. We further characterize a second extended critical phase between the Haldane and the ferromagnetic phase, as also having prevalent quadrupolar correlations, albeit with a different wavevector.The outline of this paper is as follows. In the first part we present various numerical results providing evidence for an extended critical phase without spontaneous dimerization for θ ∈ (−3π/4, −0.67π]. We show that the quintuplet gap vanishes over this whole interval and that the transition between the dimerized and the critical phase is of a generalized Beresinski-KosterlitzThouless (BKT) type. The absence of finite dimerization is discussed. We further determine conformal field theory parameters, such as scaling dimensions and the central charge for the critical region. Finally we address the second extended critical phase θ ∈ [+π/4, +π/2), which we exhibit to have prevailing quadrupolar correlations at wavevectors ±2π/3.Numerical techniques -Our results constitute the

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confidence: 59%

Spin nematics correlations in bilinear-biquadraticS=1spin chains

Läuchli¹,

2006

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“…The initial conjecture concerning this gapless phase favored an almost "trimerized" ground state [68,69], featuring dominant singlet correlations involving three consecutive spins. Although models can be constructed which have exactly trimerized ground states [70,71], it was shown in [72] that these are not the dominant fluctuations in the standard bilinear-biquadratic model. It was realized only recently, by combining numerical simulations with earlier field-theoretical results [73], that the extended critical phase actually has dominant antiferroquadrupolar correlations [64].…”

Section: From Chains To the Square Latticementioning

confidence: 99%

Spin Nematic Phases in Quantum Spin Systems

Penc

Läuchli

2010

Springer Series in Solid-State Sciences

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In this chapter, we explore the possibility for spin systems to develop a type of order that breaks the O(3) spin symmetry but does not have a magnetic moment. Such ordering is usually referred to as multipolar or nematic, with quadrupolar being the simplest example. These phases have been found in S D 1 Heisenberg models extended with biquadratic exchange, in certain S D 1=2 Heisenberg models with both ferromagnetic and antiferromagnetic exchange couplings, and in models with cyclic ring-exchange terms. We present theoretical and numerical methods which can be used to understand and characterize quadrupolar and nematic phases. While quadrupolar/nematic ordering is well documented in model systems, it has not yet been identified unambiguously in real materials, although there exist some promising candidates which we also review. Introduction and MaterialsMagnetism and spins are usually thought to be inseparable. It is the quantum mechanical spin of individual electrons which, through Hund's rules, forms the moment of a magnetic ion. When these magnetic ions interact, the spins usually order in the ground state, and the individual spins are oriented in a given direction in spin space. Such a state breaks spontaneously both spin-rotation and time-reversal symmetries. An essential property of quantum mechanical systems is the possibility of discovering phases which do not carry a magnetic moment and do not break timereversal symmetry. One paradigm is that spin-1/2 entities may pair into singlets, realizing valence-bond phases of different kinds [1] -in such a quantum paramagnetic phase, neither the spin-rotation nor the time-reversal symmetry is broken, as discussed in Chap. 2 by Lhuillier and Misguich. One might ask whether yet more exotic possibilities exist, for example a phase without magnetic order, but which nevertheless breaks spin-rotation symmetry. This chapter explores such a situation.In the following, we call a spin nematic any state that has no magnetic order, i.e. hS i i D 0, but still breaks the spin rotational symmetry, by virtue of a more complicated order parameter. The simplest such example is onsite quadrupolar order, where 331

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“…This phase-including the frustration process leading to it-is reminiscent of the dimerized phase of the J 1 − J 2 spin 1/2 chain for J 2 / J 1 Ն 0.2411. 10 Initially a massive trimerized phase for the spin 1 Heisenberg chain ͑J 2 / J 1 =0͒ for / 4 Ͻ Ͻ / 2 was put forward, 11,12 but later works 6,7,[13][14][15][16] showed that the region remains massless and has dominant nematic correlations. In our model the additional next nearest neighbor coupling J 2 allows us to stabilize the trimerized state.…”

Section: Trimerized Phasementioning

confidence: 99%

Spontaneous trimerization in a bilinear-biquadraticS=1zig-zag chain

Corboz

Läuchli²,

Totsuka

et al. 2007

Phys. Rev. B

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Recent theoretical studies raised the possibility of a realization of spin nematic states in the S = 1 triangular lattice compound NiGa 2 S 4 . We study the bilinear-biquadratic spin 1 chain in a zig-zag geometry by means of the density matrix renormalization group method and exact diagonalization. We present the phase diagram focusing on antiferromagnetic interactions. Adjacent to the known Haldane-double Haldane and the extended critical phase with dominant spin nematic correlations we find a trimerized phase with a nonvanishing energy gap. We discuss results for different order parameters, energy gaps, correlation functions, and the central charge, and make connection to field theoretical predictions for the phase diagram.

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Static and dynamic structure factors in the Haldane phase of the bilinear-biquadratic spin-1 chain

Cited by 30 publications

References 32 publications

Spin nematics correlations in bilinear-biquadraticS=1spin chains

Spin nematics correlations in bilinear-biquadraticS=1spin chains

Spin Nematic Phases in Quantum Spin Systems

Spontaneous trimerization in a bilinear-biquadraticS=1zig-zag chain

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