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

Journal Article · · Physical Review B
 [1];  [2];  [3];  [4]
  1. Princeton Univ., NJ (United States). Dept. of Physics
  2. Univ. of Pittsburgh, PA (United States). Dept. of Physics and Astronomy
  3. Univ. Würzburg (Germany). Inst. für Theoretische Physik und Astrophysik
  4. Princeton Univ., NJ (United States). Dept. of Physics; Univ. of California, Berkeley, CA (United States). Dept. of Physics
+ Show Author Affiliations

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 Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC02-05CH11231; SC0002140
OSTI ID:
1572789
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 23 Vol. 98; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Superconductivity from the condensation of topological defects in a quantum spin-Hall insulator journal June 2019
Fidelity as a probe for a deconfined quantum critical point journal August 2019
Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point journal September 2019
Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study journal February 2020
Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu 2 ( BO 3 ) 2 journal November 2019
Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point text January 2019

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