标题： 由有效$SU(M)$规范场引起的合成维度中的重子压缩 显示英文标题

标题： Baryon squishing in synthetic dimensions by effective $SU(M)$ gauge fields

摘要： 我们研究冷原子系统中具有合成维度（Celi等，PRL 112, 043001 (2014)) 的少体物理，该系统实现了沿合成维度的霍夫斯塔特模型和长程相互作用。 我们表明，这个问题可以映射到一个粒子系统（具有$SU(M)$对称相互作用），这些粒子在每个格点上经历$SU(M)$范德华场，以及{\em 和}非阿贝尔$SU(M)$规范势，该规范势影响它们从一个格点到另一个格点的跃迁。 这种映射揭示了生成{\em 非局部}相互作用（不同物理格点上的粒子之间的相互作用）的可能性。 它还表明，诱导味-轨道耦合的非阿贝尔规范场可以缓解范德华场的“重子破坏”效应。 对于$M$粒子，局域于格点的$SU(M)$单态重子被范德华场和非阿贝尔规范势的组合“变形”为非局域对象（“压缩”重子），我们通过分析论证和精确（数值）对角化研究明确地证明了这一效应。 这些结果不仅在多体情况下预示了丰富的相图，还表明利用冷原子系统可以解决传统凝聚态系统中难以想象的问题。 例如，我们说明该系统可以适应实现类似于$SU(M)$的随机通量模型的哈密顿量。 显示英文摘要

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.