Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Determinant formula for the field form factor in the anyonic Lieb-Liniger model

Piroli, L., Scopa, S., Pasquale Calabrese

Published Oct 1, 2020• 9 citations
OpenAlex

Abstract

We derive an exact formula for the field form factor in the anyonic Lieb-Liniger model, valid for arbitrary values of the interaction $c$, anyonic parameter $\kappa$, and number of particles $N$. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of a $N\times N$ matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on $\kappa$. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb-Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.

Related papers

Determinant formula for the field form factor in the anyonic Lieb–Liniger model

Lorenzo Piroli, Stefano Scopa, Pasquale Calabrese

Abstract We derive an exact formula for the field form factor in the anyonic Lieb–Liniger model, valid for arbitrary values of the interaction c, anyonic parameter κ, and number of particles N. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of an N × N matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on κ. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb–Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.

arXiv:2002.12629•Journal of Physics A Mathematical and Theoretical•May 20, 2020•5 citations

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

Lorenzo Piroli, Pasquale Calabrese

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 and Ψ R (0), for arbitrary integer R , where 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.

arXiv:1506.06539•Journal of Physics A Mathematical and Theoretical•Oct 20, 2015•44 citations

One-particle dynamical correlations in the one-dimensional Bose gas

Jean-Sébastien Caux, Pasquale Calabrese, Nikita A Slavnov

The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb–Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is well adapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case.

arXiv:cond-mat/0611321•Journal of Statistical Mechanics Theory and Experiment•Jan 8, 2007•147 citations

One-particle dynamical correlations in the one-dimensional Bose gas

Jean-Sébastien Caux, Pasquale Calabrese, Nikita A

Abstract. The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb-Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is welladapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case. One-particle dynamical correlations in the one-dimensional Bose gas 2 1.

•Jan 1, 2006•88 citations

One-dimensional impenetrable anyons in thermal equilibrium: II. Determinant representation for the dynamic correlation functions

Ovidiu I Pâţu, Vladimir E Korepin, D. V. Averin

We have obtained a determinant representation for the time- and temperature-dependent field–field correlation function of the impenetrable Lieb–Liniger gas of anyons through direct summation of the form factors. In the static case, the obtained results are shown to be equivalent to those that follow from the anyonic generalization of Lenard's formula.

arXiv:0803.0750•Journal of Physics A Mathematical and Theoretical•May 28, 2008•54 citations

Exact matrix elements of the field operator in the thermodynamic limit of the Lieb–Liniger model

Eldad Bettelheim

Abstract We study a matrix element of the field operator in the Lieb–Liniger model using the Bethe ansatz technique coupled with a functional approach to compute Slavnov determinants. We obtain the matrix element exactly in the thermodynamic limit for any coupling constant c , and compare our results to known semiclassics at the limit c → 0

arXiv:2104.08749•Journal of Physics A Mathematical and Theoretical•Aug 13, 2021•0 citations
We derive an exact formula for the field form factor in the anyonic Lieb-Liniger model, valid for arbitrary values of the interaction ccc, anyonic parameter κ\kappaκ, and number of particles NNN. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of a N×NN\times NN×N matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on κ\kappaκ. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb-Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.
Abstract We derive an exact formula for the field form factor in the anyonic Lieb–Liniger model, valid for arbitrary values of the interaction c, anyonic parameter κ, and number of particles N. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of an N × N matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on κ. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb–Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.
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 and Ψ R (0), for arbitrary integer R , where 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.
The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb–Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is well adapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case.
Abstract. The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb-Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is welladapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case. One-particle dynamical correlations in the one-dimensional Bose gas 2 1.