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

TL;DR

This paper investigates the stability of the Wilson-Fisher fixed point under quenched disorder in a large-N quantum O(2N) model, revealing a new quantum critical point with finite disorder and interactions that aligns with numerical superfluid-Mott glass transition results.

Contribution

It demonstrates that disorder effects are screened at the Wilson-Fisher fixed point, leading to a directly accessible quantum critical point with specific critical exponents, contrasting earlier spiraling flow results.

Findings

Identification of a stable quantum critical point with finite disorder and interactions.

Critical exponents match numerical superfluid-Mott glass transition data.

Analysis of disorder stability and duality conjectures for N=1 theories.

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 $N=1$.