Scaling law for the size dependence of a finite-range quantum gas

In a recent work [Reible et al., Phys. Rev. Res. 5, 023156 (2023)], it was shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite-range interactions that model dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free-energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria.

Figure 1

Interface free energy and its upper and lower bounds for two weakly coupled linear oscillator chains, each of which consists of $n=m=100$ particles. Here $\varepsilon$ is the coupling parameter that models the strength of the bilinear interactions between the 100th particle and the 101st particle (the energy is in a.u.).