Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points
Abstract
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.
- Authors:
-
- 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
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1572789
- Alternate Identifier(s):
- OSTI ID: 1484552
- Grant/Contract Number:
- AC02-05CH11231; SC0002140; AC02-05-CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 23; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Ippoliti, Matteo, Mong, Roger S. K., Assaad, Fakher F., and Zaletel, Michael P. Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points. United States: N. p., 2018.
Web. doi:10.1103/physrevb.98.235108.
Ippoliti, Matteo, Mong, Roger S. K., Assaad, Fakher F., & Zaletel, Michael P. Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points. United States. https://doi.org/10.1103/physrevb.98.235108
Ippoliti, Matteo, Mong, Roger S. K., Assaad, Fakher F., and Zaletel, Michael P. Wed .
"Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points". United States. https://doi.org/10.1103/physrevb.98.235108. https://www.osti.gov/servlets/purl/1572789.
@article{osti_1572789,
title = {Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points},
author = {Ippoliti, Matteo and Mong, Roger S. K. and Assaad, Fakher F. and Zaletel, Michael P.},
abstractNote = {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.},
doi = {10.1103/physrevb.98.235108},
journal = {Physical Review B},
number = 23,
volume = 98,
place = {United States},
year = {Wed Dec 05 00:00:00 EST 2018},
month = {Wed Dec 05 00:00:00 EST 2018}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 19 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Critical behavior in the cubic dimer model at nonzero monomer density
journal, January 2014
- Sreejith, G. J.; Powell, Stephen
- Physical Review B, Vol. 89, Issue 1
Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions
journal, June 2007
- Sandvik, Anders W.
- Physical Review Letters, Vol. 98, Issue 22
From an antiferromagnet to a valence bond solid: evidence for a first-order phase transition
journal, February 2008
- Jiang, F-J; Nyfeler, M.; Chandrasekharan, S.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2008, Issue 02
Scaling dimensions of higher-charge monopoles at deconfined critical points
journal, November 2015
- Sreejith, G. J.; Powell, Stephen
- Physical Review B, Vol. 92, Issue 18
Revisiting the hybrid quantum Monte Carlo method for Hubbard and electron-phonon models
journal, February 2018
- Beyl, Stefan; Goth, Florian; Assaad, Fakher F.
- Physical Review B, Vol. 97, Issue 8
Competing orders, nonlinear sigma models, and topological terms in quantum magnets
journal, August 2006
- Senthil, T.; Fisher, Matthew P. A.
- Physical Review B, Vol. 74, Issue 6
Hybrid Stochastic Differential Equations Applied to Quantum Chromodynamics
journal, December 1985
- Duane, Simon; Kogut, John B.
- Physical Review Letters, Vol. 55, Issue 25
Canted antiferromagnetic and spin-singlet quantum Hall states in double-layer systems
journal, August 1998
- Das Sarma, S.; Sachdev, Subir; Zheng, Lian
- Physical Review B, Vol. 58, Issue 8
Wess-Zumino-Witten Terms in Graphene Landau Levels
journal, June 2015
- Lee, Junhyun; Sachdev, Subir
- Physical Review Letters, Vol. 114, Issue 22
Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians
journal, June 2013
- Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
- Physical Review Letters, Vol. 110, Issue 23
Continuous Quantum Phase Transition between an Antiferromagnet and a Valence-Bond Solid in Two Dimensions: Evidence for Logarithmic Corrections to Scaling
journal, April 2010
- Sandvik, Anders W.
- Physical Review Letters, Vol. 104, Issue 17
Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points
journal, June 2009
- Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M.
- Physical Review Letters, Vol. 102, Issue 25
Phase diagram for the quantum Hall state in monolayer graphene
journal, April 2012
- Kharitonov, Maxim
- Physical Review B, Vol. 85, Issue 15
Emergent photons and transitions in the sigma model with hedgehog suppression
journal, August 2004
- Motrunich, Olexei I.; Vishwanath, Ashvin
- Physical Review B, Vol. 70, Issue 7
Deconfined Criticality: Generic First-Order Transition in the SU(2) Symmetry Case
journal, August 2008
- Kuklov, A. B.; Matsumoto, M.; Prokof’ev, N. V.
- Physical Review Letters, Vol. 101, Issue 5
Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
journal, October 2004
- Senthil, T.; Balents, Leon; Sachdev, Subir
- Physical Review B, Vol. 70, Issue 14
Dynamical flavor symmetry breaking by a magnetic field in 2+1 dimensions
journal, October 1995
- Gusynin, V. P.; Miransky, V. A.; Shovkovy, I. A.
- Physical Review D, Vol. 52, Issue 8
Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
journal, December 2013
- Young, A. F.; Sanchez-Yamagishi, J. D.; Hunt, B.
- Nature, Vol. 505, Issue 7484
Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
journal, December 2015
- Nahum, Adam; Chalker, J. T.; Serna, P.
- Physical Review X, Vol. 5, Issue 4
Tensor-product state approach to spin- square antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality
journal, August 2016
- Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank
- Physical Review B, Vol. 94, Issue 7
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap
journal, September 2016
- Nakayama, Yu; Ohtsuki, Tomoki
- Physical Review Letters, Vol. 117, Issue 13
Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
journal, November 2017
- Sato, Toshihiro; Hohenadler, Martin; Assaad, Fakher F.
- Physical Review Letters, Vol. 119, Issue 19
Possibility of deconfined criticality in SU( ) Heisenberg models at small
journal, December 2013
- Harada, Kenji; Suzuki, Takafumi; Okubo, Tsuyoshi
- Physical Review B, Vol. 88, Issue 22
Theta-terms in nonlinear sigma-models
journal, March 2000
- Abanov, A. G.; Wiegmann, P. B.
- Nuclear Physics B, Vol. 570, Issue 3
Impurity spin texture at a deconfined quantum critical point
journal, October 2010
- Banerjee, Argha; Damle, Kedar; Alet, Fabien
- Physical Review B, Vol. 82, Issue 15
The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code
journal, January 2017
- Bercx, Martin; Goth, Florian; Hofmann, Johannes Stephan
- SciPost Physics, Vol. 3, Issue 2
Even-denominator fractional quantum Hall states at an isospin transition in monolayer graphene
journal, July 2018
- Zibrov, A. A.; Spanton, E. M.; Zhou, H.
- Nature Physics, Vol. 14, Issue 9
Antiferromagnetic to valence-bond-solid transitions in two-dimensional Heisenberg models with multispin interactions
journal, November 2009
- Lou, Jie; Sandvik, Anders W.; Kawashima, Naoki
- Physical Review B, Vol. 80, Issue 18
Walking, weak first-order transitions, and complex CFTs
journal, October 2018
- Gorbenko, Victor; Rychkov, Slava; Zan, Bernardo
- Journal of High Energy Physics, Vol. 2018, Issue 10
Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere
journal, June 2011
- Jafferis, Daniel L.; Klebanov, Igor R.; Pufu, Silviu S.
- Journal of High Energy Physics, Vol. 2011, Issue 6
SO(5) symmetry in the quantum Hall effect in graphene
journal, December 2014
- Wu, Fengcheng; Sodemann, Inti; Araki, Yasufumi
- Physical Review B, Vol. 90, Issue 23
Deconfined Quantum Critical Points: Symmetries and Dualities
journal, September 2017
- Wang, Chong; Nahum, Adam; Metlitski, Max A.
- Physical Review X, Vol. 7, Issue 3
Continuous Easy-Plane Deconfined Phase Transition on the Kagome Lattice
journal, March 2018
- Zhang, Xue-Feng; He, Yin-Chen; Eggert, Sebastian
- Physical Review Letters, Vol. 120, Issue 11
Quantum phase transitions in bilayer SU( ) antiferromagnets
journal, May 2012
- Kaul, Ribhu K.
- Physical Review B, Vol. 85, Issue 18
Néel-State to Valence-Bond-Solid Transition on the Honeycomb Lattice: Evidence for Deconfined Criticality
journal, August 2013
- Pujari, Sumiran; Damle, Kedar; Alet, Fabien
- Physical Review Letters, Vol. 111, Issue 8
Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies
journal, June 1993
- Sondhi, S. L.; Karlhede, A.; Kivelson, S. A.
- Physical Review B, Vol. 47, Issue 24
Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
journal, March 2015
- Pujari, Sumiran; Alet, Fabien; Damle, Kedar
- Physical Review B, Vol. 91, Issue 10
Infinite density matrix renormalization group for multicomponent quantum Hall systems
journal, January 2015
- Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
- Physical Review B, Vol. 91, Issue 4
Lattice Model for the Néel to Valence-Bond Solid Quantum Phase Transition at Large
journal, March 2012
- Kaul, Ribhu K.; Sandvik, Anders W.
- Physical Review Letters, Vol. 108, Issue 13
Corrections to scaling in the critical theory of deconfined criticality
journal, November 2013
- Bartosch, Lorenz
- Physical Review B, Vol. 88, Issue 19
Canted Antiferromagnetic Phase of the Quantum Hall State in Bilayer Graphene
journal, July 2012
- Kharitonov, Maxim
- Physical Review Letters, Vol. 109, Issue 4
Scaling of entanglement support for matrix product states
journal, July 2008
- Tagliacozzo, L.; de Oliveira, Thiago. R.; Iblisdir, S.
- Physical Review B, Vol. 78, Issue 2
Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition
journal, December 2015
- Nahum, Adam; Serna, P.; Chalker, J. T.
- Physical Review Letters, Vol. 115, Issue 26
Many-Body Spin Berry Phases Emerging from the -Flux State: Competition between Antiferromagnetism and the Valence-Bond-Solid State
journal, July 2005
- Tanaka, Akihiro; Hu, Xiao
- Physical Review Letters, Vol. 95, Issue 3
Simple Fermionic Model of Deconfined Phases and Phase Transitions
journal, December 2016
- Assaad, F. F.; Grover, Tarun
- Physical Review X, Vol. 6, Issue 4
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
- Dyer, Ethan; Mezei, Márk; Pufu, Silviu S.
- Journal of High Energy Physics, Vol. 2015, Issue 6
Scaling in the Fan of an Unconventional Quantum Critical Point
journal, January 2008
- Melko, Roger G.; Kaul, Ribhu K.
- Physical Review Letters, Vol. 100, Issue 1
Quantum criticality with two length scales
journal, March 2016
- Shao, H.; Guo, W.; Sandvik, A. W.
- Science, Vol. 352, Issue 6282
Deconfined Criticality Flow in the Heisenberg Model with Ring-Exchange Interactions
journal, May 2013
- Chen, Kun; Huang, Yuan; Deng, Youjin
- Physical Review Letters, Vol. 110, Issue 18
Spontaneous interlayer coherence in double-layer quantum Hall systems: Charged vortices and Kosterlitz-Thouless phase transitions
journal, February 1995
- Moon, K.; Mori, H.; Yang, Kun
- Physical Review B, Vol. 51, Issue 8
Works referencing / citing this record:
Superconductivity from the condensation of topological defects in a quantum spin-Hall insulator
journal, June 2019
- Liu, Yuhai; Wang, Zhenjiu; Sato, Toshihiro
- Nature Communications, Vol. 10, Issue 1
Fidelity as a probe for a deconfined quantum critical point
journal, August 2019
- Sun, Gaoyong; Wei, Bo-Bo; Kou, Su-Peng
- Physical Review B, Vol. 100, Issue 6
Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study
journal, February 2020
- Li, Bo-Hai; Li, Zi-Xiang; Yao, Hong
- Physical Review B, Vol. 101, Issue 8
Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical
journal, November 2019
- Lee, Jong Yeon; You, Yi-Zhuang; Sachdev, Subir
- Physical Review X, Vol. 9, Issue 4
Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
text, January 2019
- Huang, Rui-Zhen; Lu, Da-Chuan; You, Yi-Zhuang
- arXiv