CMSA Quantum Matter in Mathematics and Physics: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids


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September 7, 2022 9:00 am - 10:30 am
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Zhengyan Darius Shi - MIT

Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity \sigma(\omega) \sim \omega^{-2/z} (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result \sigma(\omega) \sim \omega^{-2(z-2)/z}  due to Kim et al. is incorrect for inversion-odd order parameters.

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