Particle-hole pairs and density–density correlations in the Lieb–Liniger model

Nardis, Jacopo De; Panfil, Miłosz

doi:10.1088/1742-5468/aab012

Cited by 49 publications

(101 citation statements)

References 88 publications

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“…This relation was found first for the thermodynamic form factor of the density operator in the Lieb-Liniger gas[120]. We here make the conjecture that this form is universal for any local operator.…”

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confidence: 61%

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Diffusion in generalized hydrodynamics and quasiparticle scattering

2019

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We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be reached via a gradient expansion of the expectation values of the conserved fields and how the coefficients of the expansion can be computed via integrated steadystate two-point correlation functions, emphasising that PT -symmetry can fully fix the inherent ambiguity in the definition of conserved fields at the diffusive scale. We develop a form factor expansion to compute such correlation functions and we show that, while the dynamics at the Euler scale is completely determined by the density of single quasiparticle excitations on top of the local steady state, diffusion is due to scattering processes among quasiparticles, which are only present in truly interacting systems. We then show that only two-quasiparticle scattering processes contribute to the diffusive dynamics. Finally we employ the theory to compute the exact spin diffusion constant of a gapped XXZ spin−1/2 chain at finite temperature and half-filling, where we show that spin transport is purely diffusive.

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confidence: 61%

“…Single-particle-hole form factors. Single-particle-hole form factors of local densities and currents do not contain singularities and their small momentum limit is given only in terms of thermodynamic functions [120,141] lim…”

Section: Particle-hole Excitations and Correlation Functionsmentioning

confidence: 99%

Diffusion in generalized hydrodynamics and quasiparticle scattering

2019

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“…Second, an approach for the computation of correlation functions similar to the one we are describing here has already proven to be successful in the study of correlation functions of the non-relativistic Lieb Liniger model [44][45][46]. In this model, form factors with an arbitrary number of particle excitations are known from using algebraic Bethe ansatz techniques [37].…”

Section: Jhep01(2019)104mentioning

confidence: 97%

“…However certain progress in this direction was achieved in [56,59]. Here, following the logic presented in [44] and further developed in [45,46], we approximate the sum over soft modes by simply picking one specific, reference state. The choice of this state is operator dependent and it also might depend on the excitationsθ 1 , .…”

Section: Jhep01(2019)104mentioning

confidence: 99%

Thermodynamic bootstrap program for integrable QFT’s: form factors and correlation functions at finite energy density

Cubero

Panfil

2019

J. High Energ. Phys.

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We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.

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“…An important ingredient in this formulation is an assumption on the form of the leading 2-particle-hole pair form factor. The conjectured form that was put forward in [31] was inspired by the results of [32] for the thermodynamic limit of the density operator form factor in the non-relativistic integrable Lieb-Liniger model. Specifically, in formulating the Navier-Stokes GHD, it was assumed that the leading diverging part of the 2 particle-hole form factor is universal for any local operator.…”

Section: Introductionmentioning

confidence: 99%

Generalized hydrodynamics regime from the thermodynamic bootstrap program

Cubero

Panfil

2020

SciPost Phys.

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Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field theories, we show the same correlators can be computed as a sum over form factors, the GHD regime corresponding to the leading contribution with one particle-hole pair on a finite energy-density background. The thermodynamic bootstrap program (TBP) formalism was recently introduced as an axiomatic approach to computing such finite-energy-density form factors for integrable field theories. We derive a new axiom within the TBP formalism from which we easily recover the predicted GHD Eulerian correlators. We also compute higher form factor contributions, with more particle-hole pairs, within the TBP, allowing for the computation of correlation functions in the diffusive, and beyond, GHD regimes. The two particle-hole form factors agree with expressions recently conjectured within the GHD.

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Particle-hole pairs and density–density correlations in the Lieb–Liniger model

Cited by 49 publications

References 88 publications

Diffusion in generalized hydrodynamics and quasiparticle scattering

Diffusion in generalized hydrodynamics and quasiparticle scattering

Thermodynamic bootstrap program for integrable QFT’s: form factors and correlation functions at finite energy density

Generalized hydrodynamics regime from the thermodynamic bootstrap program

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