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.
Highlights
Dimensionality plays a crucial role in the study of many-body quantum physics
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
Due to the anyonic fractional statistics, the computation of correlation functions in the anyonic Lieb–Liniger gas presents additional difficulties with respect to the bosonic case, which can be studied by means of standard tools within the algebraic Bethe ansatz [78] (ABA)
Summary
Dimensionality plays a crucial role in the study of many-body quantum physics. For instance, the well-known Fermi liquid theory breaks down in one-dimension, due to the drastic effects of interactions compared to the higher dimensional case [1]. Due to the anyonic fractional statistics, the computation of correlation functions in the anyonic Lieb–Liniger gas presents additional difficulties with respect to the bosonic case, which can be studied by means of standard tools within the algebraic Bethe ansatz [78] (ABA) For this reason, instead of tackling the computation directly in the anyonic model, we map the form factor to the matrix element of the bosonic field between two special off-shell Bethe states (which will be defined ). Instead of tackling the computation directly in the anyonic model, we map the form factor to the matrix element of the bosonic field between two special off-shell Bethe states (which will be defined ) This allows us to make use of standard techniques within the ABA formalism, and follow the strategy developed in reference [64], where a set of determinant formulas were derived in the bosonic case.
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