Next-nearest-neighbour correlation functions of the spin-1/2<i>XXZ</i>chain at the critical region

We show how correlation functions of the spin-1/2 Heisenberg chain without magnetic field in the anti-ferromagnetic ground state can be explicitly calculated using information contained in the quantum Knizhnik-Zamolodchikov equation [qKZ]. We find several fundamental relations which the inhomogeneous correlations should fulfill. On the other hand, it turns out that these relations can fix the form of the correlations uniquely. Actually, applying this idea, we have obtained all the correlation functions on five sites. Particularly by taking the homogeneous limit, we have got the analytic form of the fourth-neighbor pair correlator S z j S z

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“…In papers [30,31,32] the above results were generalized to the XXZ Heisenberg chain both in massless and in massive regime.…”

Section: Introductionmentioning

confidence: 95%

First principle approach to correlation functions of spin- Heisenberg chain: fourth-neighbor correlators

2005

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“…In general, it is unknown. However, one can restore these matrix elements from the known exact expression for NNN spin correlator in the ground state |ψ 0 (α) at J = 0 and some small value of α [33]:…”

Section: Perturbation Theory For Easy-plane Case At J < 1/4mentioning

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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“…In addition, their results were extended to XXZ chain both in massless and massive regime [16,17,18].…”

Section: Introductionmentioning

confidence: 98%

Correlation functions of the spin-1/2 antiferromagnetic Heisenberg chain: Exact calculation via the generating function

2005

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Analytical expressions of some of the spin-spin correlation functions up to eight lattice sites for the spin-1/2 anti-ferromagnetic Heisenberg chain at zero temperature without magnetic field are obtained. The key object of our method is the generating function of two-point spin-spin correlators, whose functional relations are derived from those for general inhomogeneous correlation functions previously obtained from the quantum Knizhnik-Zamolodchikov equations. We show how the generating functions are fully determined by their functional relations, which leads to the two-point spinspin correlators. The obtained analytical results are numerically confirmed by the exact diagonalization for finite systems.

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Next-nearest-neighbour correlation functions of the spin-1/2XXZchain at the critical region

Cited by 44 publications

References 20 publications

First principle approach to correlation functions of spin- Heisenberg chain: fourth-neighbor correlators

First principle approach to correlation functions of spin- Heisenberg chain: fourth-neighbor correlators

Weakly anisotropic frustrated zigzag spin chain

Correlation functions of the spin-1/2 antiferromagnetic Heisenberg chain: Exact calculation via the generating function

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