有效$SU(M)$规范场在合成维中的重子压缩
Baryon squishing in synthetic dimensions by effective $SU(M)$ gauge fields
摘要：
我们研究了具有合成维度的冷原子系统中的几体物理学（Celi等人，PRL 112，043001（2014）），其实现了具有沿合成维度的长程相互作用的Hofstadter模型。我们表明，这个问题可以映射到一个质点系（与$SU(M)$对称相互作用），经历一个$SU(M)$塞曼场在每个晶格站点{ \em和}一个非阿贝尔$SU(M)$规范位，影响他们从一个网站跳到另一个。这种映射带来了产生{ \em非局部}相互作用（不同物理位点处的粒子之间的相互作用）的可能性。研究还表明，非阿贝尔规范场引起的味轨耦合，减轻了塞曼场的“重子破缺”效应。对于$M$粒子，$SU(M)$单重态重子，这是网站本地化，是“变形”的非局域对象（“压扁”重子）的组合的塞曼和非阿贝尔规范位，一个效果，我们最终证明了分析参数和精确（数值）对角化研究。这些结果不仅保证了在多体环境中的丰富相图，而且还表明了使用冷原子系统来解决传统凝聚态系统中无法想象的问题的可能性。作为一个例子，我们表明，该系统可以适应实现类似于$SU(M)$随机通量模型的哈密顿算子。
英文摘要：
We investigate few body physics in a cold atomic system with synthetic dimensions (Celi et al., PRL 112, 043001 (2014)) which realizes a Hofstadter model with long-ranged interactions along the synthetic dimension. We show that the problem can be mapped to a system of particles (with $SU(M)$ symmetric interactions) which experience an $SU(M)$ Zeeman field at each lattice site {\em and} a non-Abelian $SU(M)$ gauge potential that affects their hopping from one site to another. This mapping brings out the possibility of generating {\em non-local} interactions (interaction between particles at different physical sites). It also shows that the non-Abelian gauge field, which induces a flavor-orbital coupling, mitigates the "baryon breaking" effects of the Zeeman field. For $M$ particles, the $SU(M)$ singlet baryon which is site localized, is "deformed" to be a nonlocal object ("squished" baryon) by the combination of the Zeeman and the non-Abelian gauge potential, an effect that we conclusively demonstrate by analytical arguments and exact (numerical) diagonalization studies. These results not only promise a rich phase diagram in the many body setting, but also suggests possibility of using cold atom systems to address problems that are inconceivable in traditional condensed matter systems. As an example, we show that the system can be adapted to realize Hamiltonians akin to the $SU(M)$ random flux model.
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