Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points
- Princeton Univ., NJ (United States). Dept. of Physics
- Univ. of Pittsburgh, PA (United States). Dept. of Physics and Astronomy
- Univ. Würzburg (Germany). Inst. für Theoretische Physik und Astrophysik
- Princeton Univ., NJ (United States). Dept. of Physics; Univ. of California, Berkeley, CA (United States). Dept. of Physics
In this paper, 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 $$\mathrm{O}(5)$$ 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 $$\mathrm{O}(5)$$ vector operator to be in the range $$\mathrm{Δ_V}$$ ~ $0.55-0.7$, 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.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- AC02-05CH11231; SC0002140; AC02-05-CH11231
- OSTI ID:
- 1572789
- Alternate ID(s):
- OSTI ID: 1484552
- Journal Information:
- Physical Review B, Vol. 98, Issue 23; ISSN 2469-9950
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical
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