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.

Determinant formula for the field form factor in the anyonic Lieb-Liniger model / Piroli, L.; Scopa, S.; Calabrese, P.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 53:40(2020), pp. 1-23. [10.1088/1751-8121/ab94ed]

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

#### 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2020
53
40
1
23
405001
https://arxiv.org/abs/2002.12629
Piroli, L.; Scopa, S.; Calabrese, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.11767/117237`
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