On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain

Kozłowski, Karol K.

doi:10.48550/arxiv.1811.06076

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…Altogether the thermodynamic limit of the form factors generally results in rather technical expressions which can be seen as multiple residues related to the zeros of the counting functions of the massive excitations in the respective ground state regimes [16,48]. In spite of the technically complicated nature of the expressions for the form factors, the series derived in [48] could be used for a detailed analysis of the space-time asymptotics of the dynamical two-point functions of the XXZ chain in the antiferromagnetic massless regime at finite magnetic field [49] and of the threshold singularities of their Fourier transforms [47]. This analysis confirmed and refined, from a microscopic point of view, the non-linear Luttinger liquid phenomenology (for a review see [29]).…”

Section: Introductionmentioning

confidence: 99%

A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime

Babenko,

Göhmann,

Kozlowski

et al. 2020

Preprint

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We consider the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime. It has a series representation based on the form factors of the quantum transfer matrix of the model. The nth summand of the series is a multiple integral accounting for all n-particle n-hole excitations of the quantum transfer matrix. In previous works the expressions for the form factor amplitudes appearing under the integrals were either again represented as multiple integrals or in terms of Fredholm determinants. Here we obtain a representation which reduces, in the zero-temperature limit, essentially to a product of two determinants of finite matrices whose entries are known special functions. This will facilitate the further analysis of the correlation function.

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Section: Introductionmentioning

confidence: 99%

A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime

Babenko,

Göhmann,

Kozlowski

et al. 2020

Preprint

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“…In practice, the complexity of the Bethe ansatz wave functions means that such calculations are extremely difficult and new mathematical methods need to be devised. Initial attempts focused on the case of systems equivalent with free fermions [5][6][7][8][15][16][17][18][19][20][21][22][23][24][25][26][27] but very recently results were obtained for the Lieb-Liniger [28][29][30][31][32][33][34][35][36][37][38] and the XXZ spin-chain [39][40][41][42][43][44][45][46][47][48][49][50][51] models away from the free fermion point. Analytical derivations of the low-energy asymptotics of correlation functions are important because they can be compared with the predictions of TLL but they can also provide insight and identify systems not described by TLL theory.…”

Section: Introductionmentioning

confidence: 99%

Correlation functions of one-dimensional strongly interacting two-component gases

Pâţu¹

2019

Phys. Rev. A

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We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitute the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution n(k) at zero temperature does not present algebraic singularities but the tails obey the universal decay lim k→±∞ n(k) ∼ C/k 4 with the amplitude C given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

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Investigating the roots of the nonlinear Luttinger liquid phenomenology

Markhof

Pletyukhov²,

Meden³

2019

Preprint

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On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain

Cited by 3 publications

References 20 publications

A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime

A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime

Correlation functions of one-dimensional strongly interacting two-component gases

Investigating the roots of the nonlinear Luttinger liquid phenomenology

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