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

We propose a method to regulate (2+1)-dimensional quantum critical points in which the ultraviolet cutoff is implemented by Landau level quantization, rather than by a lattice [1]. This allows numerical computations on arbitrary manifolds without introducing lattice defects. We focus on N=4 flavors (corresponding to the spin and valley degrees of freedom of electrons in graphene) at half filling, and introduce appropriate interaction anisotropies in flavor space to drive different types of magnetic order. We thus obtain a continuum regularization of the O(5) nonlinear sigma model (NLSM) with a topological term, which has been conjectured to flow to a deconfined critical point. We perform infinite-cylinder DMRG [2] simulations of this model and estimate the dimension of the O(5) vector to be Δ_V ≈ 0.55 - 0.70, depending on the NLSM stiffness. This dependence may be a finite-size effect or further evidence of a weakly discontinuous transition. As the model is sign-problem-free, forthcoming quantum Monte Carlo simulations may be able to discriminate between these cases.

[1] M. Ippoliti, R.S.K. Mong, F.F. Assaad, M.P. Zaletel, arXiv:1810.00009 (2018)
[2] M.P. Zaletel et al., PRB 91, 045115 (2015)