We study a system of strongly interacting one-dimensional (1D) bosons on a ring pierced by a synthetic magnetic flux tube. By the Fermi-Bose mapping, this system is related to the system of spin-polarized non-interacting electrons confined on a ring and pierced by a solenoid (magnetic flux tube). On the ring there is an external localized delta-function potential barrier $V(\varphi )=g\delta (\varphi -{\varphi }_0)$. We study the Berry phase associated to the adiabatic motion of delta-function barrier around the ring as a function of the strength of the potential $g$ and the number of particles $N$. The behavior of the Berry phase can be explained via quantum mechanical reflection and tunneling through the moving barrier which pushes the particles around the ring. The barrier produces a cusp in the density to which one can associate a missing charge $\Delta q$ (missing density) for the case of electrons (bosons, respectively). We show that the Berry phase (i.e., the Aharonov-Bohm phase) cannot be identified with the quantity $\Delta q/\hslash \oint 𝐀\cdot d𝐥$. This means that the missing charge cannot be identified as a (quasi)hole. We point out to the connection of this result and recent studies of synthetic anyons in noninteracting systems. In addition, for bosons we study the weakly-interacting regime, which is related to the strongly interacting electrons via Fermi-Bose duality in 1D systems.

中文翻译：

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一维环上Bose气体的Berry相

我们研究了由合成磁通管刺穿的环上的强相互作用一维（1D）玻色子的系统。通过费米-玻色（Fermi-Bose）映射，该系统与自旋极化非相互作用电子系统相关，该电子被限制在一个环上并被螺线管（磁通管）刺穿。环上有一个外部局部三角函数势垒$V（\varphi ）=G\delta （\varphi -{\varphi }_0）$。我们研究了与三角函数势垒绕环绝热运动相关的贝里相随势强度的变化$G$ 和粒子数 $ñ$。贝里相的行为可以通过量子力学反射和穿过移动势垒的隧穿来解释，该势垒将粒子推向环。势垒在密度上产生了尖峰，可以使丢失的电荷与之相关$\Delta q$对于电子（分别为玻色子），（密度缺失）。我们证明了贝里相（即Aharonov-Bohm相）无法用数量来识别$\Delta q/\hslash \oint 𝐀\cdot d𝐥$。这意味着不能将丢失的电荷识别为（准）孔。我们指出了这一结果与非相互作用系统中合成正离子的最新研究之间的联系。此外，对于玻色子，我们研究了弱相互作用机制，该机制与在一维系统中通过费米-玻色对偶性的强相互作用电子有关。