Universal Properties of Anisotropic Dipolar Bosons in Two Dimensions

TL;DR

This paper investigates the universal behavior of two-dimensional dipolar bosons, revealing scaling laws at large gas parameters and analyzing how anisotropic interactions influence their ground state properties.

Contribution

It demonstrates that dipolar bosons exhibit universal scaling laws at large gas parameters, extending understanding beyond typical regimes and accounting for anisotropic interactions.

Findings

Scaling laws hold up to large gas parameters

Universal behavior persists near phase transition boundaries

Anisotropy affects the scattering length dependence

Abstract

The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter $x=n a_0^d$, with $n$ the density, $d$ the dimensionality of the space ($d=1,2,3$) and $a_0$ the $s$-wave scattering length. The universal regime typically extends up to $x\approx 0.001$, while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes $a_0$ depend on the polarization angle $\alpha$, so different combinations of $n$ and $\alpha$ can lead to the same value of the gas parameter $x$. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large values of the gas parameter $x$. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of $x$ that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.