拓扑有序生长量子态
Growing quantum states with topological order
摘要：
本文讨论了在相互作用多体系统中，利用通量量子序列和粒子插入来生长具有拓扑序的态的方案。我们首先考虑一个简单的玩具模型，超晶格玻色哈伯德模型，解释所有需要的成分。我们的协议，然后应用到分数量子霍尔系统，连续和晶格。我们特别调查的保真度，与拓扑有序的状态可以增长，尺度与粒子数N的增加。对于小系统，使用精确对角化方法。为了处理大系统的许多粒子，我们引入了一个有效的模型的基础上的复合费米子描述的分数量子霍尔效应。该模型还允许考虑系统中色散带和边缘的影响，这将在下文中详细讨论。
英文摘要：
We discuss a protocol for growing states with topological order in interacting many-body systems using a sequence of flux quanta and particle insertion. We first consider a simple toy model, the superlattice Bose Hubbard model, to explain all required ingredients. Our protocol is then applied to fractional quantum Hall systems in both, continuum and lattice. We investigate in particular how the fidelity, with which a topologically ordered state can be grown, scales with increasing particle number N. For small systems exact diagonalization methods are used. To treat large systems with many particles, we introduce an effective model based on the composite fermion description of the fractional quantum Hall effect. This model also allows to take into account the effects of dispersive bands and edges in the system, which will be discussed in detail.
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