强关联格点玻色子的非微扰重整化群方法
Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
摘要：
本文对玻色-哈伯德模型提出了一种非微扰的重整化群方法。通过将解耦点的（局部）极限作为重整化群流的初始条件，我们以非平凡的方式同时考虑了局部和长距离的涨落。这种方法产生的相图在很好的定量协议与量子蒙特卡罗模拟，并再现两个普适类的超流体-莫特绝缘体过渡。在多临界点附近的临界行为，即在恒定密度下发生转变的地方，与Fisher { \it et al.}的原始预测一致。[Phys. Rev. B { \bf 40}，546（1989）]基于简单的缩放参数。在一个通用的过渡点，临界行为是平均场的对数修正在二维。在弱关联超流相（远离Mott绝缘相），重整化群流受Bogoliubov不动点控制，降到特征（Ginzburg）动量尺度$k_G$，远小于逆愈合长度$k_h$ .在附近的多临界点，当密度是相称的，我们确定了一个尖锐的交叉从弱到强相关的超流相的凝聚体密度和超流刚度被强烈抑制和$k_G$和$k_h$的顺序的逆晶格间距。
英文摘要：
We present a nonperturbative renormalization-group approach to the Bose-Hubbard model. By taking as initial condition of the renormalization-group flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial way. This approach yields a phase diagram in very good quantitative agreement with quantum Monte Carlo simulations, and reproduces the two universality classes of the superfluid--Mott-insulator transition. The critical behavior near the multicritical points, where the transition takes place at constant density, agrees with the original predictions of Fisher {\it et al.} [Phys. Rev. B {\bf 40}, 546 (1989)] based on simple scaling arguments. At a generic transition point, the critical behavior is mean-field like with logarithmic corrections in two dimensions. In the weakly-correlated superfluid phase (far away from the Mott insulating phase), the renormalization-group flow is controlled by the Bogoliubov fixed point down to a characteristic (Ginzburg) momentum scale $k_G$ which is much smaller than the inverse healing length $k_h$. In the vicinity of the multicritical points, when the density is commensurate, we identify a sharp crossover from a weakly- to a strongly-correlated superfluid phase where the condensate density and the superfluid stiffness are strongly suppressed and both $k_G$ and $k_h$ are of the order of the inverse lattice spacing.
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