用Hubbard二聚体对最简单的从粒子理论进行基准测试
Benchmarking the simplest slave-particle theory with Hubbard dimer
摘要：
从粒子方法是解决量子多体物理中关联效应的有力工具。虽然它已经成功地用于理解各种有趣的问题，如莫特金属-绝缘体转变和近藤效应，仍然没有令人信服的理论，迄今为止，该方法的有效性和局限性。滥用从粒子方法可能导致错误的物理学。$\mathbb{Z}_2$从自旋方法作为一种最简单的从粒子方法，具有很强的可操作性和研究性，在强关联问题中有着广泛的应用。在这项工作中，我们将揭示$\mathbb{Z}_2$从自旋方法的性质，通过研究两个网站的哈伯德模型。在探讨了这个玩具模型的一些性质之后，我们对三种方法得到的结果进行了比较分析：（i）平均场水平上的slave-spin方法，（ii）规范约束下的slave-spin方法和（iii）作为基准的精确解.我们发现，在粒子-空穴对称性的保护下，从自旋平均场方法可以精确地恢复半填充时基态的静态性质。此外，在$U$和$T$都足够小的参数空间中，从自旋平均场方法在计算动力学和热力学性质时也是可靠的。然而，当$U$或$T$相当大时，平均场近似给出了定义不清的行为，这是由于在扩大的希尔伯特空间中的非物理状态。这些结果表明，如果通过规范约束排除所有非物理态，从粒子方法的精度是可以保证的，这表明从粒子方法在研究具有特定对称性或特定参数空间的复杂强关联模型中具有广阔的应用前景。
英文摘要：
Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal-insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, $\mathbb{Z}_2$ slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of $\mathbb{Z}_2$ slave-spin method by studying a two-site Hubbard model. After exploring some properties of this toy model, we make a comparative analysis of the results obtained by three methods: (i) slave-spin method on mean-field level, (ii) slave-spin method with gauge constraint and (iii) the exact solution as a benchmark. We find that, protected by particle-hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both $U$ and $T$ are small enough, slave-spin mean-field method is also reliable in calculating dynamic and thermal dynamic properties. However, when $U$ or $T$ is considerably large, the mean-field approximation gives ill-defined behavior, which results from the unphysical states in enlarged Hilbert space. These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints.Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.
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