A quantum field-theoretical perspective on scale anomalies in 1D systems with three-body interactions

Abstract

We analyze, from a canonical quantum field theory perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in two-dimensional systems with two-body interactions. We study in detail the properties of the scattering amplitude including both bound and scattering states, using cutoff and dimensional regularization, and clarify the connection between the scale anomaly derived from thermodynamics to the non-vanishing nonrelativistic trace of the energy-momentum tensor.

Three-body interaction near a narrow two-body zero crossing

“…In particular, three-body forces have been considered in the context of droplet formation in three dimensions [16][17][18][19] and as a means for stabilizing supersolid phases of quasi-two-dimensional dipolar atoms or molecules [20]. Quite a few recent theory papers have discussed one-dimensional three-bodyinteracting systems, exploring the kinematic equivalence of the three-body scattering in one dimension and the two-body scattering in two dimensions (see, for example [21][22][23][24][25][26][27][28][29][30][31][32]).…”

Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions

“…When the coupling constant is dimensionless, a new length scale emerges from quantum effects called dimensional transmutation [46]. In nonrelativistic QFT, the dimensional transmutation is discussed in 1D [47][48][49][50] and 2D [51] cases. However, since the 1D scattering length a is only the length scale associated with the contact interaction, the emergence of an additional scale is prohibited in our case.…”

Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

“…Motivated by the recent interest in one-dimensional (1D) Fermi and Bose gases in the fine-tuned situation where only three-body interactions are present [1][2][3][4][5][6][7][8][9], we explore here the thermodynamics of fermions with a contact three-body interaction in the region of low fugacity (which corresponds to a dilute regime and therefore high temperatures in units of the energy scale set by the density). We focus on the fermionic case but explore the problem in arbitrary dimension d. To that end, we implement a semiclassical lattice approximation (SCLA) to calculate the virial coefficients b n , and carry out their evaluation up to n = 5 at leading order (LO) in that approximation.…”