Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point

Abstract

We study the stability of the Wilson-Fisher fixed point of the quantum $\mathrm{O}(2N)$ vector model to quenched disorder in the large-$N$ limit. While a random mass is strongly relevant at the Gaussian fixed point, its effect is screened by the strong interactions of the Wilson-Fisher fixed point. This enables a perturbative renormalization group study of the interplay of disorder and interactions about this fixed point. We show that, in contrast to the spiralling flows obtained in earlier double-$\epsilon$ expansions, the theory flows directly to a quantum critical point characterized by finite disorder and interactions. The critical exponents we obtain for this transition are in remarkable agreement with numerical studies of the superfluid-Mott glass transition. We additionally discuss the stability of this fixed point to scalar and vector potential disorder and use proposed boson-fermion dualities to make conjectures regarding the effects of weak disorder on dual Abelian Higgs and Chern-Simons-Dirac fermion theories when $N=1$.

arXiv comment47 pages, including seven figures and three appendices

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• Quantum phase transitions in Dirac fermion systems
• Interaction-induced metallicity in a two-dimensional disordered non-Fermi liquid
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• Renormalization group in quantum critical theories with Harris-marginal disorder
• Disordered quantum critical fixed points from holography
• A Bound on Thermalization from Diffusive Fluctuations
• Scaling and Diffusion of Dirac Composite Fermions
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• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Quenched random mass disorder in the large N theory of vector bosons
• Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals