Low-energy effective field theories of fermion liquids and the mixed U(1)×Rd anomaly
Low-energy effective field theories of fermion liquids and the mixed U(1)×Rd anomaly
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DOI：
10.1103/physrevb.103.165126
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发表时间：
2021-04
影响因子：
3.7
通讯作者：
X. Wen
中科院分区：
文献类型：
--
作者：
X. Wen
本文研究了具有粒子数守恒和平移对称性的维连续空间中无间隙费米子和玻色子系统。提出了几种具有对称性的无间隙相的低能有效场理论。对称有一个特性，即不对称扭转会引起与电荷密度成正比的非零动量，这将被称为混合异常。同一系统不同相的不同有效场论必须具有相同的混合异常。因此，所有的低能量有效场论都必须具有数量级的非零动量场。特别地，我们提出了具有无限多场的费米液体的低能量有效场论。我们还提出了存在真实空间磁场和k空间“磁场”以及存在由朗道参数描述的相互作用时的费米-液体有效场理论。我们的有效场论正确地捕获了混合异常，这限制了低能动力学，例如根据混合异常确定费米表面的体积[即根据电荷密度]。这是Luttinger-Ward-Oshikawa定理的另一种表述。
In this paper, we study gapless fermionic and bosonic systems in-dimensional continuum space withparticle-number-conservation andtranslation symmetry. We present low-energy effective field theories for several gapless phases with thesymmetry. Thesymmetry has a property that asymmetry twist will induce a nonzero momentum proportional to thecharge density, which will be referred to as a mixed anomaly. The different effective field theories for different phases of the same system must have the same mixed anomaly. As a result, all the low-energy effective field theories must have fields with nonzero momenta of the order of. In particular, we present a low-energy effective field theory with infinite number of fields for Fermi liquid. We also present the Fermi-liquid effective field theory in the presence of a real space magnetic field and k-space “magnetic” field, as well as in the presence of interaction described by Landau parameters. Our effective field theory correctly captures the mixed anomaly, which constrains the low-energy dynamics, such as determines the volume of the Fermi surface in terms of the mixed anomaly [i.e., in terms of thecharge density]. This is another formulation of the Luttinger-Ward-Oshikawa theorem.