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

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