Thermodynamics and static response of anomalous 1D fermions via quantum Monte Carlo in the worldline representation

A system of three-species fermions in one spatial dimension (1D) with a contact three-body interaction is known to display a scale anomaly. This anomaly is identical to that of a two-dimensional (2D) system of two-species fermions. The exact relation between those two systems, however, is limited to the two-particle sector of the 2D case and the three-particle sector of the 1D case. Here, we implement a non-perturbative Monte Carlo approach, based on the worldline representation, to calculate the thermodynamics and static response of three-species fermions in 1D, thus tackling the many-body sector of the problem. We determine the energy, density, and pressure equations of state, and the compressibility and magnetic susceptibility for a wide range of temperatures and coupling strengths. We compare our results with the third-order virial expansion.