标题： 分数霍尔层次结构来自对偶性 显示英文标题

标题： The Fractional Hall hierarchy from duality

摘要： 我们证明了Seiberg等人提出的Son的狄拉克复合费米子理论的修改版本，为单个Landau能级内的禁带和非禁带分数量子霍尔态提供了一个统一的描述候选。 我们的主要工具是对复合费米子的部分填充Landau能级连续应用三维对偶性，这表明该理论具有复杂的禁带真空和临界点的景观。 这个构造是通量附加过程的拉格朗日或有效场论模拟。 临界点存在于偶分母填充情况下，并且可以通过一个弱耦合的复合费米子与阿贝尔Chern-Simons理论耦合的费米面来很好地描述。 禁带状态包括奇分母填充分数状态，其具有阿贝尔Chern-Simons描述，我们证明它与层次状态所预期的描述相匹配，还包括从复合费米子费米面的对不稳定性的偶分母填充下的非阿贝尔状态。 显示英文摘要

摘要： We show that a modified version of Son's Dirac composite fermion theory proposed by Seiberg et al gives a candidate unified description of the gapped and gapless fractional quantum Hall states within a single Landau level. Our main tool is the successive application of three-dimensional dualities to partially filled Landau levels of composite fermions, which imply that this theory has a complicated landscape of gapped vacua and critical points. This construction is the Lagrangian, or effective field theory, analogue of the flux attachment procedure. The critical points exist at even denominator filling and are well-described by a Fermi surface for a weakly coupled composite fermion coupled to an abelian Chern-Simons theory. The gapped states include odd-denominator filling fraction states with an abelian Chern-Simons description which we show matches the one expected for hierarchy states, as well as non-abelian states at even-denominator filling that arise from pair instabilities of the composite fermion's Fermi surface.