On the finite volume expectation values of local operators in the sine-Gordon model

Hegedűs, Árpád

doi:10.1016/j.nuclphysb.2019.114749

Cited by 5 publications

(6 citation statements)

References 66 publications

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“…There have been active work and relevant progress in deriving finite volume one-point functions for the exponential operators and their descendants in these theories [23,24]. These results were then extended for diagonal matrix elements in the sine-Gordon theory [25,26,27] and the aim of our paper is to provide similar expressions in the sinh-Gordon theory.The paper is organized as follows: Section 2 reviews the description of the finite size energy spectrum of the sinh-Gordon theory. A multi-particle state for large volumes can be labelled by momentum quantum numbers, which we relate at small volume to the spectrum of the Liouville conformal field theory by matching the eigenvalues of the conserved charges.…”

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Diagonal finite volume matrix elements in the sinh-Gordon model

Bajnok

Смирнов

2019

Nuclear Physics B

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Using the fermionic basis we conjecture exact expressions for diagonal finite volume matrix elements of exponential operators and their descendants in the sinh-Gordon theory. Our expressions sum up the LeClair-Mussardo type infinite series generalized by Pozsgay for excited state expectation values. We checked our formulae against the Liouville three-point functions for small, while against Pozsgay's expansion for large volumes and found complete agreement. * Membre du CNRS the ground-state TBA densities with the excited state ones and contains additional factors, which can be interpreted as partial density of states [20,21].Alternatively, there is an other approach which focuses on specific theories and exploits their hidden (Grassmann) structure to provide compact expressions for finite volume matrix elements [22]. These specific continuum models arise as limits of integrable lattice models and the most studied examples are the sinh-Gordon and sine-Gordon models. There have been active work and relevant progress in deriving finite volume one-point functions for the exponential operators and their descendants in these theories [23,24]. These results were then extended for diagonal matrix elements in the sine-Gordon theory [25,26,27] and the aim of our paper is to provide similar expressions in the sinh-Gordon theory.The paper is organized as follows: Section 2 reviews the description of the finite size energy spectrum of the sinh-Gordon theory. A multi-particle state for large volumes can be labelled by momentum quantum numbers, which we relate at small volume to the spectrum of the Liouville conformal field theory by matching the eigenvalues of the conserved charges. In Section 3 we formulate our main conjecture for the finite volume exceptions values in the fermionic basis. The novelty compared to the vacuum expectation values is the discrete part of the convolutions, which carries information on the particles' rapidities. We check this conjecture for large volumes in Section 4. The discrete part of the convolution contains the polynomial, while the continuous part the exponentially small corrections in the volume. In Section 5 we compare our conjecture with Liouville three-point functions for low lying states including non-degenerate and degenerate L 0 subspaces. All the checks performed confirm our conjecture, thus we close the paper with conclusions in Section 6.

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Diagonal finite volume matrix elements in the sinh-Gordon model

Bajnok

Смирнов

2019

Nuclear Physics B

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“…Our method could be helpful in finding new results. Also, it would be interesting to consider the sine-Gordon model, whose finite volume mean values were investigated in [80,81]. As far as we know, it is not yet clear whether a finite volume expansion theorem exists in that model.…”

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The LeClair-Mussardo series and nested Bethe Ansatz

Hutsalyuk,

Pozsgay,

Pristyák

2020

Preprint

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We consider correlation functions in one dimensional quantum integrable models related to the algebra symmetries gl(2|1) and gl(3). Using the algebraic Bethe Ansatz approach we develop an expansion theorem, which leads to an infinite integral series in the thermodynamic limit. The series is the generalization of the LeClair-Mussardo series to nested Bethe Ansatz systems, and it is applicable both to one-point and two-point functions. As an example we consider the ground state density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi particles. Explicit formulas are presented in a special large coupling and large imbalance limit.

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“…To sum up, to find the energy of the antiferromagnetic vacuum of the lattice model, we first solve Equation ( 24) to find the counting function Z N (u) and then compute the energy and momentum by (28).…”

Section: Energy and Momentummentioning

confidence: 99%

TT¯ Deformation: A Lattice Approach

Jiang

2023

Symmetry

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Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theories on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between a sine-Gordon model and a six-vertex model on a light-cone lattice. We propose an integrable deformation of the light-cone lattice model such that in the continuum limit we obtain the TT¯-deformed sine-Gordon model. Under this deformation, the cut-off momentum becomes energy dependent and the underlying Yang–Baxter integrability is preserved. Therefore, this deformation is integrable but non-local: similar to the TT¯ deformation of quantum field theory.

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On the finite volume expectation values of local operators in the sine-Gordon model

Cited by 5 publications

References 66 publications

Diagonal finite volume matrix elements in the sinh-Gordon model

Diagonal finite volume matrix elements in the sinh-Gordon model

The LeClair-Mussardo series and nested Bethe Ansatz

TT¯ Deformation: A Lattice Approach

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