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We perform density-matrix renormalization group studies of a two-dimensional electron gas in a high magnetic field and with an anisotropic band mass. At half-filling in the lowest Landau level, such a system is a Fermi liquid of composite fermions. By measuring the Fermi surface of these composite fermions, we determine a relationship between the anisotropy of composite fermion dispersion, αCF , and the original anisotropy αF of the fermion dispersion at zero magnetic field. For systems where the electrons interact via a Coulomb interaction, we find αCF = √ αF within our numerical accuracy. The same result has been found concurrently in recent experiments. We also find that the relationship between the anisotropies is dependent on the form of the electron-electron interaction.

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 ∆V ∼ 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.arXiv:1810.00009v1 [cond-mat.str-el]