Phase diagram of the<i>XXZ</i>chain with next-nearest-neighbor interactions

Somma, Rolando D.; Aligia, A. A.

doi:10.1103/physrevb.64.024410

Cited by 50 publications

(53 citation statements)

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“…3,4,5,6,7,8 By contrast, relatively less is understood for the case of ferromagnetic (FM) J 1 and AF J 2 despite earlier studies. 9,10,11,12 Recently, interest has been growing in this FM J 1 case because of its possible relevance . Some of these compounds exhibit multiferroic behavior in low-temperature spiral spin ordered phases, where the long-range order (LRO) of the vector spin chirality produces the electric polarization.…”

Section: Introductionmentioning

confidence: 99%

COMPETING PHASES IN SPIN-½ J₁-J₂ CHAIN WITH EASY-PLANE ANISOTROPY

et al. 2011

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We summarize our theoretical findings on the ground-state phase diagram of the spin-1 2 XXZ chain having competing nearest-neighbor (J 1 ) and antiferromagnetic next-nearestneighbor (J 2 ) couplings. Our study is mainly concerned with the case of ferromagnetic J 1 , and the case of antiferromagnetic J 1 is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J 1 /J 2 versus the XXZ anisotropy ∆: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga-Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J 1 side.

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Section: Introductionmentioning

confidence: 99%

COMPETING PHASES IN SPIN-½ J₁-J₂ CHAIN WITH EASY-PLANE ANISOTROPY

et al. 2011

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“…For example, the phase diagram of the model (1) with ∆ 1 = ∆ 2 has been studied in Ref. [26] using the method of level spectroscopy. Unfortunately, this method becomes unreliable for J ≈ 1/4 and ∆ 1 = ∆ 2 ≈ 1 because of strong finite-size effects.…”

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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“…For the quarterfilled chain, the Kondo lattice model has a dimerized phase. This can be understood from the phase diagram of the effective and suitable values of the nearest-neighbor interaction [14]. Our results for the dependence of the critical temperature p on the Kondo interaction 1 do not depend on the specific type of magnetic order.…”

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confidence: 62%

Ordering temperature and thermodynamic properties of Kondo systems

Lobos

Aligia

2005

phys. stat. sol. (c)

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We consider a system of Kondo impurities with an RKKY interaction ¡ between them. Using the exact solution of the impurity and approximating the effect of but then decreases and vanishes at a quantum critical point (QCP). The approach is useful to calculate thermodynamic properties of Kondo systems out of the QCP.In the past three decades, a large amount of experimental and theoretical work was devoted to the understanding of the Kondo lattice. A review of theoretical results in one dimension is given in Ref. [1]. In spite of this effort, the general form of a solution in more dimensions has not been found and phenomenological approaches [2], based on exact solutions for the impurity [3,4] are still been used for the description of Kondo systems. The nature of the ground state in Kondo lattice materials depends on the competition between two energy scales: the single impurity Kondo temperature, and the RKKY interaction , the physics is dominated by the effective exchange interaction between localized spins, and the system orders magnetically. In agreement with these observations, using a mean-field approximation for the one-dimensional system, Doniach obtained a second-order transition from an antiferromagnetic (AF) ground state for low 1 ) to a non-magnetic Kondo singlet for large 1 ). The temperature of magnetic order and the competition between single ion spin compensation and interatomic RKKY interaction has also been calculated in more dimensions using mean-field approximations [6,7]. However, comparison with numerical results in one dimension suggest that the mean-field phase diagram is incorrect [1].We propose that as long as lattice effects discussed later are not too important, the thermodynamic properties of the system can be described by a model which corresponds to a collection of Kondo impurities interacting via an effective exchange interaction in YbS NiT AlU [8]. The data below 150 K have a shape similar to the exact results for a Kondo impurity with total angular momentum 7/2 (corresponding to Yb K. However, the latter should be multiplied by a factor near 1/3 to fit the experiments. This points to a strong AF interaction 1 between the Yb ions. However, the system does not order due to the dominance of the single ion e

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Phase diagram of theXXZchain with next-nearest-neighbor interactions

Cited by 50 publications

References 25 publications

COMPETING PHASES IN SPIN-½ J₁-J₂ CHAIN WITH EASY-PLANE ANISOTROPY

COMPETING PHASES IN SPIN-½ J₁-J₂ CHAIN WITH EASY-PLANE ANISOTROPY

Weakly anisotropic frustrated zigzag spin chain

Ordering temperature and thermodynamic properties of Kondo systems

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Phase diagram of theXXZchain with next-nearest-neighbor interactions

Cited by 50 publications

References 25 publications

COMPETING PHASES IN SPIN-½ J1-J2 CHAIN WITH EASY-PLANE ANISOTROPY

COMPETING PHASES IN SPIN-½ J1-J2 CHAIN WITH EASY-PLANE ANISOTROPY

Weakly anisotropic frustrated zigzag spin chain

Ordering temperature and thermodynamic properties of Kondo systems

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Product

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COMPETING PHASES IN SPIN-½ J₁-J₂ CHAIN WITH EASY-PLANE ANISOTROPY

COMPETING PHASES IN SPIN-½ J₁-J₂ CHAIN WITH EASY-PLANE ANISOTROPY