论文标题
某些量子厅系统中的非交通性场理论和复合费米液体
Non-commutative field theory and composite Fermi Liquids in some quantum Hall systems
论文作者
论文摘要
复合费米液体金属在量子厅制度的某些特殊填充部分出现，并作为具有量化霍尔响应的ged状态的父状态发挥重要作用。它们是由Halperin-Lee-Read Read（HLR）理论成功地描述的，该理论的复合费米斯的费米表面与Chern-Simons术语结合到$ u（1）$ gauge字段。但是，当微观系统仅限于单个Landau时，HLR描述的有效性尚不清楚。在这里，对于玻色子的特定情况，填充$ν= 1 $，我们以1990年代的早期工作为基础，以制定低能描述，该描述采用了{\ em nontocutative}字段理论的形式。该理论具有复合费米斯的费米表面，该复合费用耦合到$ u（1）$ gauge字段，没有Chern-simons项，但其特征是所有字段均在非交换时空定义。长波长，小幅度量规波动的近似映射产生了一个交换的有效场理论，它显着地采用了HLR形式，但具有微观参数，由相互作用强度正确确定。讨论了一些其他复合费米液体以及其他相关物质状态的扩展。
Composite Fermi liquid metals arise at certain special filling fractions in the quantum Hall regime and play an important role as parent states of gapped states with quantized Hall response. They have been successfully described by the Halperin-Lee-Read (HLR) theory of a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with a Chern-Simons term. However, the validity of the HLR description when the microscopic system is restricted to a single Landau has not been clear. Here for the specific case of bosons at filling $ν= 1$, we build on earlier work from the 1990s to formulate a low energy description that takes the form of a {\em non-commutative} field theory. This theory has a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with no Chern-Simons term but with the feature that all fields are defined in a non-commutative spacetime. An approximate mapping of the long wavelength, small amplitude gauge fluctuations yields a commutative effective field theory which, remarkably, takes the HLR form but with microscopic parameters correctly determined by the interaction strength. Extensions to some other composite fermi liquids, and to other related states of matter are discussed.
