Zhengyan Darius Shi, Dominic V. Else, Hart Goldman, T. Senthil
SciPost Phys. 14, 113 (2023) ·
published 15 May 2023

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We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the "HertzMillis" type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving $N$ species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequencydependent conductivity at the IR fixed point, $\sigma(\omega>0)\sim\omega^{2/z}$, where $z$ is the boson dynamical exponent. Leveraging the nonperturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomalyassisted large $N$ expansion" allows us to extract the conductivity systematically. Although our results imply that such randomflavor models are problematic as a description of the physical $N = 1$ system, they serve to illustrate some general conditions for quantum critical transport as well as the anomalyassisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequencydependent conductivity, $\sigma(\omega>0) \sim \omega^{2(z2)/z}$, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.
Benjamin Moy, Hart Goldman, Ramanjit Sohal, Eduardo Fradkin
SciPost Phys. 14, 023 (2023) ·
published 27 February 2023

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A longstanding problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional $\Theta$angles, longrange entanglement, and fractionalization. Starting from a simple family of $\mathbb{Z}_N$ lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyonsâ€”bound states of electric charges and monopolesâ€”condense, leading to FTI phases characterized by topological order, emergent oneform symmetries, and gapped boundary states not realizable in 2+1D alone. Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating oneform and twoform gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal "generalized magnetoelectric effect" in the presence of twoform background gauge fields. Moreover, we characterize the possible boundary topological orders of oblique TIs, finding a new set of boundary states not studied previously for these kinds of TQFTs.
Zhengyan Darius Shi, Hart Goldman, Dominic V. Else, T. Senthil
SciPost Phys. 13, 102 (2022) ·
published 1 November 2022

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NonFermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, nonperburbative results can be obtained for both optical transport and static susceptibilities in "HertzMillis" theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, $\mathbf{q}=0$, is a constant independent of frequency, and the real part of the optical conductivity, $\sigma(\omega)$, is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.