Evolution between quantum Hall and conducting phases: Simple models and some results
Evolution between quantum Hall and conducting phases: Simple models and some results
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DOI：
10.1103/physrevb.105.085301
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发表时间：
2021-07
影响因子：
3.7
通讯作者：
Z. Dong;T. Senthil
中科院分区：
文献类型：
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作者：
Z. Dong;T. Senthil
量子多粒子系统中的动能，强相关性，和带拓扑结构都是重要的，提出了一个有趣的和局部的挑战。在这里，我们介绍和研究特别简单的模型，其中所有这些元素都存在。考虑了强磁场中二维量子粒子的相互作用，使得希尔伯特空间被限制在最低朗道能级（LLL）。这是熟悉的量子霍尔机制，具有由粒子填充和统计确定的丰富物理学。一个周期势的单胞包围一个通量量子的LLL扩展到一个有限带宽的陈带。在量子霍尔区得到的态在大带宽的极限下演化为导电态。我们详细研究了填充因子ν = 1的玻色子的这种演化。在量子霍尔体系中，在这种填充下的基态是带隙的量子霍尔态（“玻色子费米”），它可以被视为从（玻色子）复合费米液体下降。在大带宽下，基态是玻色超流体。我们展示了如何在一个单一的理论框架内描述这两个阶段及其演变的基础上，一个LLL复合费米子建设。基于我们以前对玻色子复合费米液体的研究，我们证明了在周期势场中，非对易量子场论可以有效地描述超流体的演化。
Quantum many particle systems in which the kinetic energy, strong correlations, and band topology are all important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the Lowest Landau Level (LLL) . This is the familiar quantum Hall regime with rich physics determined by the particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor ν = 1. In the quantum Hall regime the ground state at this filling is a gapped quantum hall state (the “bosonic Pfaffian”) which may be viewed as descending from a (bosonic) composite fermi liquid. At large bandwidth the ground state is a bosonic superfluid. We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite fermi liquid, we show that the evolution into the superfluid can be usefully described by a noncommutative quantum field theory in a periodic potential.