Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain

Dugave, Maxime; Göhmann, Frank; Kozłowski, Karol K.

doi:10.1088/1742-5468/2014/04/p04012

Cited by 40 publications

(80 citation statements)

References 43 publications

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“…In that case, one uses a determinant presentation for the norm and the scalar product of BVs [5,6] to get an easy-tohandle expression for the form factors. The latter then can be used to study the thermodynamic limit of the form factors and get insight on the correlation functions asymptotic behavior [7,8].…”

Section: Introductionmentioning

confidence: 99%

Bethe vectors for models based on the super-Yangian $\boldsymbol{Y}(\mathfrak{gl}\boldsymbol{(m|n))}$

Pakuliak

Ragoucy

Slavnov

2017

Journal of Integrable Systems

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We study Bethe vectors of integrable models based on the super-Yangian Y (gl(m|n)). Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of Y (gl(2|1)) and Y (gl(1|2)). These recursion relations allow to get explicit expressions for the Bethe vectors. Using an antimorphism of the super-Yangian Y (gl(m|n)), we also construct a super-trace formula for dual Bethe vectors, and, for Y (gl(2|1)) and Y (gl(1|2)) super-Yangians, show recursion relations for them. Again, the latter allow us to get explicit expressions for dual Bethe vectors.However for models based on higher rank Lie algebras (or their quantum deformation), much less is known. Already at the level of BVs, although the ABA was performed long ago [9], few explicit expressions have been obtained, apart from the scalar product obtained in [10] that is difficult to handle. Recently, in a series of papers, the case of gl(3) and of its quantum deformation was successfully studied, starting from explicit forms for BVs [11,12] and the calculation of their scalar products [13,14], up to determinant presentations for form factors [15]. The case of Bose gas with two internal degrees of freedom was also tackled, again with explicit expressions for Bethe vectors [16,17], and determinant presentations of the form factors [18,19,20]. The case of more general Lie algebra (or their quantum deformation) remains to be done, but some steps have been done towards their resolution, using the current presentation of these algebras [21]. Note also that a trace formula for BVs is known for the gl(n) [22] that can be used to deduce more properties of Bethe vectors.The case of superalgebras is even less rich, apart from a super-trace formula in the gl(m|n) case [23]. It is rather unfortunate, given their relevance in the study of gauge theories [24,25,26], in particular super-Yang-Mills (SYM) theories and AdS/CFT correspondence (see [27] and references therein). Indeed it is now believed that integrability should play an important role in SYM theories based on P SL(4|4) [28], and also in its subsectors, such as P SL(2|2) or SL(2|1) [29]. Moreover, the t-J model, well-known in condensed matter physics, is based on the gl(2|1) superalgebra [30]. Thus, there is some urge to find explicit representations for the Bethe vectors for integrable models based on these superalgebras. The aim of this paper is to present explicit expressions for Bethe vectors of integrable models based on gl(2|1) and gl(1|2).The method we will be using mimics the one used for the gl(3). Starting from the supertrace formula, we will deduce some recursion relations obeyed by the BVs. Then, solving these recursions, we will obtain explicit expressions for BVs. Using different morphisms, we will use the solution for the Y (gl(2|1)) case to construct solutions for the Y (gl(1|2)) case and also for the dual BVs.The plan of our paper follows the lines we mentioned. After reminding some properties of Yangians Y (gl(m|n)), based on gl(m|n) Lie superalgebras in section 2, we ...

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Section: Introductionmentioning

confidence: 99%

Bethe vectors for models based on the super-Yangian $\boldsymbol{Y}(\mathfrak{gl}\boldsymbol{(m|n))}$

Pakuliak

Ragoucy

Slavnov

2017

Journal of Integrable Systems

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“…Spin chains have been the center of attention as prototypical quantum many body systems ever since the early days of quantum mechanics [1] and up to this day significant advances are made, e.g. in describing exact form factors [2][3][4][5][6], exact correlations [7], nonequilibrium states [8,9], and dynamic correlations in the regime of a non-linear spectrum [10][11][12][13][14][15][16][17][18]. Recently, there has been renewed experimental interest in intentionally doped spin chain systems [19,20] with new results on the Knight shift [21,22], magnetic ordering [23], and the dynamic structure factor [24][25][26][27].…”

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confidence: 99%

Dynamic structure factor in impurity-doped spin chains

et al. 2018

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The effects of impurities in spin-1/2 Heisenberg chains are recently experiencing a renewed interest due to experimental realizations in solid state systems and ultra-cold gases. The impurities effectively cut the chains into finite segments with a discrete spectrum and characteristic correlations, which have a distinct effect on the dynamic structure factor. Using bosonization and the numerical Density Matrix Renormalization Group we provide detailed quantitative predictions for the momentum and energy resolved structure factor in doped systems. Due to the impurities, spectral weight is shifted away from the antiferromagnetic wave-vector k = π into regions which normally have no spectral weight in the thermodynamic limit. The effect can be quantitatively described in terms of scaling functions, which are derived from a recurrence relation based on bosonization.

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“…[64] and successfully applied, for instance, in Ref. [65] in the context of low-temperature, large-distance asymptotics of two-point functions of the XXZ model. In the planar regime, the kernels are regular and decay very fast at infinity.…”

Section: Asymptotic Analysis Of the Ratio Of Determinantsmentioning

confidence: 99%

Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state

Brockmann

Stéphan

2017

J. Phys. A: Math. Theor.

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We analyze universal terms that appear in the large system size scaling of the overlap between the Néel state and the ground state of the spin-1/2 XXZ chain in the antiferromagnetic regime. In a critical theory, the order one term of the asymptotics of such an overlap may be expressed in terms of g-factors, known in the context of boundary conformal field theory. In particular, for the XXZ model in its gapless phase, this term provides access to the Luttinger parameter. In its gapped phase, on the other hand, the order one term simply reflects the symmetry broken nature of the phase. In order to study the large system size scaling of this overlap analytically and to compute the order one term exactly, we use a recently derived finite-size determinant formula and perform an asymptotic expansion. Our analysis confirms the predictions of boundary conformal field theory and enables us to determine the exponent of the leading finite-size correction. arXiv:1705.08505v2 [cond-mat.stat-mech] 5 Aug 2017Universal terms in the overlap of the XXZ ground state with the Néel state

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Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain

Cited by 40 publications

References 43 publications

Bethe vectors for models based on the super-Yangian $\boldsymbol{Y}(\mathfrak{gl}\boldsymbol{(m|n))}$

Bethe vectors for models based on the super-Yangian $\boldsymbol{Y}(\mathfrak{gl}\boldsymbol{(m|n))}$

Dynamic structure factor in impurity-doped spin chains

Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state

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