Exact prefactors in static and dynamic correlation functions of one-dimensional quantum integrable models: Applications to the Calogero-Sutherland, Lieb-Liniger, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math>models

Shashi, Aditya; Panfil, Miłosz; Caux, Jean-Sébastien; Imambekov, Adilet

doi:10.1103/physrevb.85.155136

Cited by 69 publications

(130 citation statements)

References 114 publications

(176 reference statements)

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“…In all cases these exact results reproduce and generalize the predictions of the Tomonaga-Luttingerliquid-conformal-field-theory (TLL-CFT) approach [49][50][51]. * patu@spacescience.ro A method of determining the "nonuniversal" prefactors appearing in the TLL-CFT expansion was introduced in [52,53] and, also, very recently, in [54].…”

Section: Introductionsupporting

confidence: 63%

Correlation lengths of the repulsive one-dimensional Bose gas

Pâţu

Klümper

2013

Phys. Rev. A

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We investigate the large-distance asymptotic behavior of the static density-density and field-field correlation functions in the one-dimensional Bose gas at finite temperature. The asymptotic expansions of the Bose gas correlators are obtained performing a specific continuum limit in the similar low-temperature expansions of the longitudinal and transversal correlation functions of the XXZ spin chain. In the lattice system the correlation lengths are computed as ratios of the largest and next-largest eigenvalues of the XXZ spin chain quantum transfer matrix. In both cases, lattice and continuum, the correlation lengths are expressed in terms of solutions of Yang-Yang type [C.N. Yang and C.P. Yang, J.Math.Phys. 10, 1151 (1969)] non-linear integral equations which are easily implementable numerically.Comment: 35+9 pages, 7 figures, RevTeX 4.

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Section: Introductionsupporting

confidence: 63%

Correlation lengths of the repulsive one-dimensional Bose gas

Pâţu

Klümper

2013

Phys. Rev. A

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“…This can be done very efficiently for example using the so called ABACUS algorithm [18,20,53,54] The formulas presented in section 3 are also suitable for non-trivial analytical calculations as those performed in [50,51]. In these works the form factors of the operators Ψ(0), Ψ † (0)Ψ(0) were computed in the thermodynamic limit, starting from the corresponding finite size formulas derived in [15,16,17].…”

Section: Numerical Checks and Discussionmentioning

confidence: 99%

Exact formulas for the form factors of local operators in the Lieb–Liniger model

Piroli¹,

Calabrese²

2015

J. Phys. A: Math. Theor.

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Abstract. We present exact formulas for the form factors of local operators in the repulsive Lieb-Liniger model at finite size. These are essential ingredients for both numerical and analytical calculations. From the theory of Algebraic Bethe Ansatz, it is known that the form factors of local operators satisfy a particular type of recursive relations. We show that in some cases these relations can be used directly to derive practical expressions in terms of the determinant of a matrix whose dimension scales linearly with the system size. Our main results are determinant formulas for the form factors of the operators (Ψ † (0)) 2 Ψ 2 (0) and Ψ R (0), for arbitrary integer R, where Ψ, Ψ † are the usual field operators. From these expressions, we also derive the infinite size limit of the form factors of these local operators in the attractive regime.

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“…In parallel, studies of ground state dynamical correlations have recently forced us to revise our understanding of quasiparticles in critical 1D systems [12][13][14][15][16][17][18][19][20], culminating with the development of the nonlinear Luttinger liquid (NLL) theory [21]. This theory predicts that the long-time decay of correlation functions is dominated by excitations involving particles or holes near band edges, explaining the high-frequency oscillations observed numerically [22,23] and confirmed by exact form factor approaches [24,25].…”

Section: Introductionmentioning

confidence: 99%

Low temperature dynamics of nonlinear Luttinger liquids

2015

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Low temperature dynamics of nonlinear Luttinger liquidsTo cite this article: C Karrasch et al 2015 New J. Phys. 17 103003 View the article online for updates and enhancements. Related contentDynamical structure factor at small q for the XXZ spin-1/2 chain R G Pereira, J Sirker, J-S Caux et al. AbstractWe develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement. Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, G t t 1 , ( ) in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.

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Exact prefactors in static and dynamic correlation functions of one-dimensional quantum integrable models: Applications to the Calogero-Sutherland, Lieb-Liniger, andXXZmodels

Cited by 69 publications

References 114 publications

Correlation lengths of the repulsive one-dimensional Bose gas

Correlation lengths of the repulsive one-dimensional Bose gas

Exact formulas for the form factors of local operators in the Lieb–Liniger model

Low temperature dynamics of nonlinear Luttinger liquids

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