SciPost Phys. Core 8, 024 (2025) ·
published 18 February 2025
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Quantum spin liquids are exotic phases of quantum matter especially pertinent to many modern condensed matter systems. Dirac spin liquids (DSLs) are a class of gapless quantum spin liquids that do not have a quasi-particle description and are potentially realized in a wide variety of spin $1/2$ magnetic systems on $2d$ lattices. In particular, the DSL in square lattice spin-$1/2$ magnets is described at low energies by $(2+1)d$ quantum electrodynamics with $N_f=4$ flavors of massless Dirac fermions minimally coupled to an emergent $U(1)$ gauge field. The existence of a relevant, symmetry-allowed monopole perturbation renders the DSL on the square lattice intrinsically unstable. We argue that the DSL describes a stable continuous phase transition within the familiar Neel phase (or within the Valence Bond Solid (VBS) phase). In other words, the DSL is an "unnecessary" quantum critical point within a single phase of matter. Our result offers a novel view of the square lattice DSL in that the critical spin liquid can exist within either the Neel or VBS state itself, and does not require leaving these conventional states.
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 "Hertz-Millis" 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, frequency-dependent conductivity at the IR fixed point, $\sigma(\omega>0)\sim\omega^{-2/z}$, where $z$ is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large $N$ expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor 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 anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, $\sigma(\omega>0) \sim \omega^{-2(z-2)/z}$, 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.
Zhengyan Darius Shi, Hart Goldman, Dominic V. Else, T. Senthil
SciPost Phys. 13, 102 (2022) ·
published 1 November 2022
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Non-Fermi 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, non-perburbative results can be obtained for both optical transport and static susceptibilities in "Hertz-Millis" 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.
