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 (φ†(0))2φ2(0) and φR(0), for arbitrary integer R, where φ, φ† 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.

Exact formulas for the form factors of local operators in the Lieb-Liniger model / Lorenzo Piroli; Pasquale Calabrese. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - ELETTRONICO. - 48:45(2015), pp. 454002.454002-1-454002.454002-26. [10.1088/1751-8113/48/45/454002]

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

#### 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 (φ†(0))2φ2(0) and φR(0), for arbitrary integer R, where φ, φ† 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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2015
Exact formulas for the form factors of local operators in the Lieb-Liniger model / Lorenzo Piroli; Pasquale Calabrese. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - ELETTRONICO. - 48:45(2015), pp. 454002.454002-1-454002.454002-26. [10.1088/1751-8113/48/45/454002]
Lorenzo Piroli; Pasquale Calabrese
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11585/941517`
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