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arXiv 1302.7230cond-mat.quant-gas
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格点玻色子系统的复合玻色子映射

Composite Boson Mapping for Lattice Boson Systems

Daniel Huerga, Jorge Dukelsky, Gustavo E. Scuseria

摘要:

我们提出了一个规范的映射转换成二次产品的集群复合玻色子,保留矩阵元素的运营商时,强制执行的物理约束的物理玻色子运营商。我们将二维格点玻色-哈伯德哈密顿量映射到$2\times 2$复合玻色子上,并在平均场中求解。所得到的莫特绝缘体-超流相图再现量子蒙特卡罗结果。希格斯玻色子沿粒子-空穴对称线的行为被解开,并与实验非常一致。基态和激发态的性质的结果与其他国家的最先进的方法是有竞争力的,但在其计算成本的一小部分。这里介绍的复合玻色子映射可以很容易地应用于大多数方法面临重大障碍的受挫多体系统。

英文摘要:

We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into $2\times 2$ composite bosons and solve it at mean field. The resulting Mott insulator-superfluid phase diagram reproduces well Quantum Monte Carlo results. The Higgs boson behavior along the particle-hole symmetry line is unraveled and in remarkable agreement with experiment. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles.

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