Half-filled Landau levels: a continuum and sign-free regularization for 3D quantum critical points

Abstract: We explore a method for regulating 2+1D quantum critical points in which the ultra-violet cutoff is provided by the finite density of states of particles in a magnetic field, rather than by a lattice. Such Landau level quantization allows for numerical computations on arbitrary manifolds, like spheres, without introducing lattice defects. In particular, when half-filling a Landau level with $N=4$ electron flavors, with appropriate interaction anisotropies in flavor space, we obtain a fully continuum regularization of the O(5) non-linear sigma-model with a topological term, which has been conjectured to flow to a deconfined quantum critical point. We demonstrate that this model can be solved by both infinite density matrix renormalization group calculations and sign-free determinantal quantum Monte Carlo. DMRG calculations estimate the scaling dimension of the O(5) vector operator to be in the range $\Delta_V \sim 0.55 - 0.7$ depending on the stiffness of the non-linear sigma model. Future Monte Carlo simulations will be required to determine whether this dependence is a finite-size effect or further evidence for a weakly first-order transition.