Bose-Hubbard基态：扩展Bogoliubov和变分方法与时间演化块抽取的比较
The Bose-Hubbard ground state: extended Bogoliubov and variational methods compared with time-evolving block decimation
摘要：
本文研究了一维光晶格中玻色原子相互作用气体的基态性质。该系统由玻色-哈伯德哈密顿量建模。我们展示了如何将时间演化的分块抽取方法应用于周期性边界条件的系统，并将其作为参考来寻找玻色-哈伯德模型的基态。结果进行了比较，最近提出的近似方法，如Hartree-Fock-Bogoliubov（HFB）理论概括为强相互作用和变分Bijl-Dingle-Jastrow方法。我们发现，所有的HFB方法没有带来任何改善Bogoliubov理论，因此提供正确的结果，只有在弱相互作用的限制，系统是深深的超流政权。另一方面，变分Bijl-Dingle-Jastrow方法适用于更强的相互作用，但本质上是有限的超流制度，因为它再现的超流莫特绝缘体的过渡只定性。
英文摘要：
We determine the ground-state properties of a gas of interacting bosonic atoms in a one-dimensional optical lattice. The system is modelled by the Bose-Hubbard Hamiltonian. We show how to apply the time-evolving block decimation method to systems with periodic boundary conditions, and employ it as a reference to find the ground state of the Bose-Hubbard model. Results are compared with recently proposed approximate methods, such as Hartree-Fock-Bogoliubov (HFB) theories generalised for strong interactions and the variational Bijl-Dingle-Jastrow method. We find that all HFB methods do not bring any improvement to the Bogoliubov theory and therefore provide correct results only in the weakly-interacting limit, where the system is deeply in the superfluid regime. On the other hand, the variational Bijl-Dingle-Jastrow method is applicable for much stronger interactions, but is essentially limited to the superfluid regime as it reproduces the superfluid-Mott insulator transition only qualitatively.
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