Nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math>Model for Inhomogeneous Spin Chains

Takano, K.

doi:10.1103/physrevlett.82.5124

Cited by 23 publications

(32 citation statements)

References 19 publications

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“…[10]. Integrating out the fluctuations and taking the continuum limit, we finally obtain the effective action [10]:…”

Section: Nlsm For the General Spin Chainmentioning

confidence: 99%

Phase diagrams of mixed-spin chains with period 4 using the nonlinearσmodel

Takano

2000

Phys. Rev. B

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We study mixed quantum spin chains consisting of two kinds of spins with magnitudes, sa and s b . The spins are arrayed as sa-sa-s b -s b in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear σ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear σ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of sa and s b . We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.

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“…[10]. Integrating out the fluctuations and taking the continuum limit, we finally obtain the effective action [10]:…”

Section: Nlsm For the General Spin Chainmentioning

confidence: 99%

Phase diagrams of mixed-spin chains with period 4 using the nonlinearσmodel

Takano

2000

Phys. Rev. B

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“…Among these studies, the systems with unique spins and different spins in the unit cell have been found to give rise to novel quantum phases and unusual thermodynamic properties. [10][11][12][13][14][15][16][17][18][19][20] It has also been pointed out that the mixture of ferromagnetic and antiferromagnetic interactions 21-23 provides interesting properties. Many such low-dimensional molecular magnetic structures have also been synthesized.…”

mentioning

confidence: 99%

Size-dependent low-energy excitations in an alternating spin-1/spin-12antiferromagnetic chain: Spin-wave theory and density-matrix renormalization-group studies

2007

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We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-1 2 antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group ͑DMRG͒ method, and exact-diagonalization method. The ground state of this model with 2N spins is ferrimagnetic with the total spin S G = N / 2 for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin S = S G − 1. The lowest gapped excitation, however, exists in the total spin S = S G + 1 sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin S = S G + 1 is lower than that in the total spin S = S G − 1 when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.

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“…The period of the system 2b is regarded as 6 for convenience. After a standard procedure, 29 we have the effective action for the spin-͑1, 1/2, 1/2͒ Hamiltonian,…”

Section: B Haldane-like Gapmentioning

confidence: 99%

Magnetization plateaus, Haldane-like gap, string order, and hidden symmetry in a spin-12tetrameric Heisenberg antiferromagnetic chain

Gong

2008

Phys. Rev. B

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The ground-state properties of a spin S =1/ 2 tetrameric Heisenberg antiferromagnetic chain with alternating couplings AF 1 -AF 2 -AF 1 -F ͑AF and F denote antiferromagnetic and ferromagnetic couplings, respectively͒ are studied by means of the density-matrix renormalization-group method. Two plateaus of magnetization m are found at m = 0 and 1/4. It is shown that in such a spin-1/2 AF system, there is a gap from the singlet ground state to the triplet excited states in the absence of a magnetic field. The spin-spin correlation function decays exponentially, and the gapped states have a nonvanishing string order, which measures a hidden symmetry in the system. By a dual transformation, the string order is transformed into a ferromagnetic order and the hidden symmetry is unveiled to be a Z 2 ϫ Z 2 discrete symmetry, which is fully broken in the gapped states. This half-integer spin Heisenberg AF chain is in a Haldane-like phase suggesting that the present findings extend the substance of Haldane's scenario. A valence-bond-solid state picture is also proposed for the gapped states.

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NonlinearσModel for Inhomogeneous Spin Chains

Cited by 23 publications

References 19 publications

Phase diagrams of mixed-spin chains with period 4 using the nonlinearσmodel

Phase diagrams of mixed-spin chains with period 4 using the nonlinearσmodel

Size-dependent low-energy excitations in an alternating spin-1/spin-12antiferromagnetic chain: Spin-wave theory and density-matrix renormalization-group studies

Magnetization plateaus, Haldane-like gap, string order, and hidden symmetry in a spin-12tetrameric Heisenberg antiferromagnetic chain

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