Novel criticality of Dirac fermions from lattice symmetry breaking

Abstract

We consider the role of spontaneous lattice symmetry breaking in strongly interacting two dimensional Dirac systems. The fermion induced quantum (multi-)criticality is described by Dirac fermions coupled to a dynamical order parameter that is composed of mass and emergent gauge fields. This is illustrated for the example of translational symmetry breaking due to charge-density wave order on the honeycomb lattice. Using a renormalization-group analysis we find that the putative emergent Lorentz invariance is violated. Finally, we identify that topological phase transitions are well described by this effective field theory.

arXiv commentThis article is superseded by the extended version arXiv:2002.10955

References in corpus (78)

• The electronic properties of graphene
• Two and one-dimensional honeycomb structures of silicon and germanium
• "Deconfined" quantum critical points
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Gauge fields in graphene
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Topological Mott Insulators
• Interactions and phase transitions on graphene's honeycomb lattice
• Quantum Field Theory in the Large N Limit: a review
• Electron fractionalization in two-dimensional graphenelike structures
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Discovery of topological chiral crystals with helicoid arc states
• Merging of Dirac points in a two-dimensional crystal
• Theory of interacting electrons on the honeycomb lattice
• Chiral Topological Semimetal with Multifold Band Crossings and Long Fermi arcs
• Half-metallic semiDirac point generated by quantum confinement in TiO${}_2$/VO${}_2$ nanostructures
• A new magnetic field dependence of Landau levels on a graphene like structure
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• Theory of resonant multiphonon Raman scattering in graphene
• Relativistic Mott criticality in graphene
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Quantum phase transitions in d-wave superconductors
• Artificial graphene with tunable interactions
• Competing orders and quantum criticality in doped antiferromagnets
• Interaction driven instabilities of a Dirac semi-metal
• Fermion-induced quantum critical points
• Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
• Renormalization group theory of nematic ordering in d-wave superconductors
• Theory of the nodal nematic quantum phase transition in superconductors
• Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Phases of correlated spinless fermions on the honeycomb lattice
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Interaction driven phases in the honeycomb lattice from exact diagonalization
• Renormalization group analysis of quantum critical points in d-wave superconductors
• Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
• Out-of-bounds hydrodynamics in anisotropic Dirac fluids
• Fixed-point structure of low-dimensional relativistic fermion field theories: Universality classes and emergent symmetry
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Gauge-field-assisted Kekulé quantum criticality
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Correlated spinless fermions on the honeycomb lattice revisited
• Interaction-induced anomalous quantum Hall state on the honeycomb lattice
• Fermion-induced quantum criticality with two length scales in Dirac systems
• The emergence of a universal limiting speed
• Interplay of topology and electron-electron interactions in Rarita-Schwinger-Weyl semimetals
• Theory of topological quantum phase transitions in 3D noncentrosymmetric systems
• Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution
• From Birefringent Electrons to a Marginal or Non-Fermi Liquid of Relativistic Spin-1/2 Fermions: An Emergent Superuniversality
• Interaction effect in two-dimensional Dirac fermions
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions
• Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions
• Observation of topological Bloch-state defects and their merging transition
• Compatible orders and fermion-induced emergent symmetry in Dirac systems
• Non-abelian gauge fields and quadratic band touchings in molecular graphene
• Deconfined quantum criticality and emergent SO(5) symmetry in fermionic systems
• Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling
• Helical scattering signatures of strain and electronic textures in YbFe2O4 from three-dimensional reciprocal space imaging
• Phase diagram of interacting spinless fermions on the honeycomb lattice
• Superconducting States for Semi-Dirac Fermions at Zero and Finite Magnetic Fields
• Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Stabilization of Topological Insulator Emerging from Electron Correlations on Honeycomb Lattice and Its Possible Relevance in Twisted Bilayer Graphene
• Quantum Criticalities with Infinite Anisotropy in Topological Phase Transitions between Dirac and Weyl Semi-metals
• Phase transition with trivial quantum criticality in anisotropic Weyl semimetal
• Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model
• Discrete symmetries of low-dimensional Dirac models: A selective review with a focus on condensed-matter realisations
• Hidden Charge Order of Interacting Dirac Fermions on the Honeycomb Lattice

Cited by in corpus (5)

• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Quantum phase transitions in Dirac fermion systems
• Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents
• Quantum Criticality of Type-I and Critically Tilted Dirac Semimetals
• Bipolaron formed through electron-hole excitation