Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points

We explore a method for regulating 2+1D quantum critical points in which the ultraviolet 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) nonlinear 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 (DMRG) 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) similar to 0.55-0.7, depending on the stiffness of the nonlinear sigma model. Future Monte Carlo simulations will be required to determine whether this dependence is a finite-size effect or further evidence for a weak first-order transition.