Pauli crystals -- interplay of symmetries

Hubbard model: Pinning of occupation numbers and role of symmetries

Fermionic natural occupation numbers do not only obey Pauli's exclusion principle, but are even further restricted by so-called generalized Pauli constraints. Such restrictions are particularly relevant whenever they are saturated by given natural occupation numbers $\vecλ=(λ_i)$. For few-site Hubbard models we explore the occurrence of this pinning effect. By varying the on-site interaction $U$ for the fermions we find sharp transitions from pinning of $\vecλ$ to the boundary of the allowed region to nonpinning. We analyze the origin of this phenomenon which turns out be either a crossing of …

泡利晶体超辐射

Pauli crystal superradiance

本文研究了腔体-费米子系统中泡利晶体的形成，揭示了泡利晶体与超辐射的关联，并通过数值模拟验证了统计、约束几何和光介导相互作用共同促进量子结晶的新路径。

Optimal configurations and "Pauli crystals" of quantum clusters

Broken rotational and translational symmetries are the hallmarks of solid state materials. In contrast, quantum liquids and gases do not exhibit such properties. However, if we regard the logarithm of the absolute square of a quantum liquid as an energy ${\cal E}= -{\rm ln}|Ψ|^2$, a geometric pattern naturally occurs at the minimum, i.e. the optimal configuration. Such geometric patterns have recently been studied for non-interacting fermions, and have been named "Pauli crystals". However, such patterns exist in all interacting gases (Bose or Fermi), independent of statistics. Here, we present…

费米子的统计势：涌现的吸引力与保罗i晶体形成

Attractive statistical forces and Pauli crystal formation in trapped Fermi gases

研究揭示了N个相同费米子的热力学可通过集体统计势解释，该势能解释了德泽压力的微观起源，且对于N≥3时产生吸引力贡献，形成保罗i晶体结构。

Pairing instabilities in quasi-two-dimensional Fermi gases

We study non-equilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from weakly interacting to strongly interacting regime. We develop a T-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a…

Topological States with Broken Translational and Time-Reversal Symmetries in a Honeycomb-Triangular Lattice

We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: both spins in a triangular lattice, and a mixed geometry with up-spins in honeycomb and down-spins in triangular lattices. We focus on the interplay between spin-population imbalance, on-site and valence bond pairing, and order parameter symmetry. The mixed geometry leads to a rich phase diagram of topologically non-trivial phases. In both geometries, we predict order parameters with simultaneous time-reversal and translational symmetry breaking.