具有平方反比相互作用的自旋模型中空和耗尽的形成几率
Emptiness and Depletion Formation Probability in spin models with inverse square interaction
摘要：
利用自旋-卡洛格罗模型（sCM）和Haldane-Shastry模型（HSM）的流体动力学描述，计算了空区形成概率（EFP）。EFP是空间区域在量子多体系统的基态中完全没有粒子的概率。我们计算这种概率的瞬子的方法，通过考虑更一般的问题的任意耗尽粒子（DFP）。在大尺寸耗尽区的限制下，概率由满足一组边界条件的虚时间中的经典配置决定，并且在这样的解上计算的作用给出指数精度的EFP/DFP。我们表明，sCM的计算可以优雅地进行表示为两个无自旋Calogero集体场论在辅助变量的总和的自旋粒子的无梯度流体动力学。有趣的是，我们在EFP中发现的结果可以用自旋-电荷分离的形式来描述，而对于这样的非线性效应，这应该是违反的。从EFP/DFP的角度，我们还强调了sCM，HSM和$λ=2$ spin-less Calogero模型之间的联系。
英文摘要：
We calculate the Emptiness Formation Probability (EFP) in the spin-Calogero Model (sCM) and Haldane-Shastry Model (HSM) using their hydrodynamic description. The EFP is the probability that a region of space is completely void of particles in the ground state of a quantum many body system. We calculate this probability in an instanton approach, by considering the more general problem of an arbitrary depletion of particles (DFP). In the limit of large size of depletion region the probability is dominated by a classical configuration in imaginary time that satisfies a set of boundary conditions and the action calculated on such solution gives the EFP/DFP with exponential accuracy. We show that the calculation for sCM can be elegantly performed by representing the gradientless hydrodynamics of spin particles as a sum of two spin-less Calogero collective field theories in auxiliary variables. Interestingly, the result we find for the EFP can be casted in a form reminiscing of spin-charge separation, which should be violated for a non-linear effect such as this. We also highlight the connections between sCM, HSM and $λ=2$ spin-less Calogero model from a EFP/DFP perspective.
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