# Many-Body Physics of Low-Density Dipolar Bosons in Box Potentials

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## Abstract

**:**

## 1. Introduction

## 2. Two-Body Physics of Dipole–Dipole Interactions

## 3. Many-Body Properties

## 4. Results

#### 4.1. Methodology

#### 4.2. Density Profile of the Filament Phase

#### 4.3. Weakly Interacting Regime

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Relation between scattering length ${a}_{s}$ and dipolar length ${a}_{d}$ in units of ${r}_{0}$, see text.

**Figure 2.**Ratio ${\u03f5}_{d}={a}_{d}/{a}_{s}$ vs. ${a}_{d}/{r}_{0}$. filled and open square and correspond to experimental parameters for ${}^{162}$Dy and ${}^{164}$Dy, respectively, with their background scattering length ($122{a}_{0}$ and $92{a}_{0}$, respectively).

**Figure 3.**(

**a**) QMC density distribution of a filament phase for $n{r}_{0}^{3}={10}^{-2}$. The number of filaments for these parameters is equal to four. Periodic boundary conditions have been employed. (

**b**) Particle density within a filament as a function of $r/{r}_{0}$. Different colors represent different filament distributions with respect to filaments of (

**a**). For these filaments, the average particle number is about ${N}_{p}=25$ (see text).

**Figure 4.**(

**top**) QMC density distribution at different strengths ${\u03f5}_{d}$ = 0.6 (

**a**), 1.2 (

**b**), 1.8 (

**c**), considering a rescaled density $n{r}_{0}^{3}=1\times {10}^{-4}$; and (

**bottom**) radial distribution functions for the corresponding configurations.

**Figure 5.**Frequency of occurrence of cycles comprising n particles at low $T/{T}_{0}$ (see text) for a system of $N=100$ particles and ${\u03f5}_{d}=1.2$.

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**MDPI and ACS Style**

Macrì, T.; Cinti, F.
Many-Body Physics of Low-Density Dipolar Bosons in Box Potentials. *Condens. Matter* **2019**, *4*, 17.
https://doi.org/10.3390/condmat4010017

**AMA Style**

Macrì T, Cinti F.
Many-Body Physics of Low-Density Dipolar Bosons in Box Potentials. *Condensed Matter*. 2019; 4(1):17.
https://doi.org/10.3390/condmat4010017

**Chicago/Turabian Style**

Macrì, Tommaso, and Fabio Cinti.
2019. "Many-Body Physics of Low-Density Dipolar Bosons in Box Potentials" *Condensed Matter* 4, no. 1: 17.
https://doi.org/10.3390/condmat4010017