Abstract
A non-relativistic fermion system interacting with a gauge field is studied by wilsonian renormalization-group analysis. This model is motivated by the work of Halperin, Lee and Read, which discussed a two-dimensional electron system in a magnetic field at the Landau filling factor v = 1 2 . A dissipative term of the gauge field (the Landau damping factor) is generated under the renormalization-group transformations, and it plays a very important role in the low-energy behaviors of the system. Renormalization constants are calculated in the one-loop level. In some parameter region, the renormalized gauge coupling constant has a non-trivial infrared fixed point, and the low-energy renormalized fermion propagator has a branch cut rather than a pole, just like the Luttinger liquid in one dimension. At a special value of the parameter, the weight of quasi-particles decreases at low energy as 1/ln ω, where ω is the energy of the fermon. This behavior is nothing but that of the marginal Fermi liquid, which is proposed to describe the anomalous metallic phase of high- T c cuprates.
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