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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
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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
Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science

References (52)

Critical behavior in the cubic dimer model at nonzero monomer density journal January 2014
Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions journal June 2007
From an antiferromagnet to a valence bond solid: evidence for a first-order phase transition journal February 2008
Scaling dimensions of higher-charge monopoles at deconfined critical points journal November 2015
Revisiting the hybrid quantum Monte Carlo method for Hubbard and electron-phonon models journal February 2018
Competing orders, nonlinear sigma models, and topological terms in quantum magnets journal August 2006
Hybrid Stochastic Differential Equations Applied to Quantum Chromodynamics journal December 1985
Canted antiferromagnetic and spin-singlet quantum Hall states in double-layer systems journal August 1998
Wess-Zumino-Witten Terms in Graphene Landau Levels journal June 2015
Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians journal June 2013
Continuous Quantum Phase Transition between an Antiferromagnet and a Valence-Bond Solid in Two Dimensions: Evidence for Logarithmic Corrections to Scaling journal April 2010
Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points journal June 2009
Phase diagram for the ν = 0 quantum Hall state in monolayer graphene journal April 2012
Emergent photons and transitions in the O ( 3 ) sigma model with hedgehog suppression journal August 2004
Deconfined Criticality: Generic First-Order Transition in the SU(2) Symmetry Case journal August 2008
Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm journal October 2004
Dynamical flavor symmetry breaking by a magnetic field in 2+1 dimensions journal October 1995
Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state journal December 2013
Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models journal December 2015
Tensor-product state approach to spin- 1 2 square J 1 − J 2 antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality journal August 2016
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap journal September 2016
Quantum Phase Transitions book January 2011
Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry journal November 2017
Possibility of deconfined criticality in SU( N ) Heisenberg models at small N journal December 2013
Theta-terms in nonlinear sigma-models journal March 2000
Impurity spin texture at a deconfined quantum critical point journal October 2010
The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code journal January 2017
Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene journal July 2018
Antiferromagnetic to valence-bond-solid transitions in two-dimensional SU ( N ) Heisenberg models with multispin interactions journal November 2009
Walking, weak first-order transitions, and complex CFTs journal October 2018
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere journal June 2011
SO(5) symmetry in the quantum Hall effect in graphene journal December 2014
Deconfined Quantum Critical Points: Symmetries and Dualities journal September 2017
Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice journal March 2018
Quantum phase transitions in bilayer SU( N ) antiferromagnets journal May 2012
Néel-State to Valence-Bond-Solid Transition on the Honeycomb Lattice: Evidence for Deconfined Criticality journal August 2013
Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies journal June 1993
Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet journal March 2015
Infinite density matrix renormalization group for multicomponent quantum Hall systems journal January 2015
Lattice Model for the SU ( N ) Néel to Valence-Bond Solid Quantum Phase Transition at Large N journal March 2012
Corrections to scaling in the critical theory of deconfined criticality journal November 2013
Canted Antiferromagnetic Phase of the ν = 0 Quantum Hall State in Bilayer Graphene journal July 2012
Scaling of entanglement support for matrix product states journal July 2008
Deconfined Quantum Critical Points journal March 2004
Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition journal December 2015
Many-Body Spin Berry Phases Emerging from the π -Flux State: Competition between Antiferromagnetism and the Valence-Bond-Solid State journal July 2005
Simple Fermionic Model of Deconfined Phases and Phase Transitions journal December 2016
Scaling dimensions of monopole operators in the ℂ ℙ N b − 1 $$ \mathbb{C}{\mathrm{\mathbb{P}}}^{N_b-1} $$ theory in 2 + 1 dimensions journal June 2015
Scaling in the Fan of an Unconventional Quantum Critical Point journal January 2008
Quantum criticality with two length scales journal March 2016
Deconfined Criticality Flow in the Heisenberg Model with Ring-Exchange Interactions journal May 2013
Spontaneous interlayer coherence in double-layer quantum Hall systems: Charged vortices and Kosterlitz-Thouless phase transitions journal February 1995

Cited By (5)

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
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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