Quantum phase transitions in Dirac fermion systems

Abstract

A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention has been paid in recent years to two-dimensional (2D) materials in which itinerant fermions acquire a pseudo-relativistic Dirac dispersion, such as graphene, topological insulator surfaces, and certain spin liquids. This article reviews the phenomenology and theoretical description of quantum phase transitions in systems of 2D Dirac fermions.

arXiv comment15 pp. + references, 1 figure; mini-review submitted to issue of Eur. Phys. J. Special Topics dedicated to proceedings of FQMT'19 conference (Prague, July 14-20, 2019). v2: published version

References in corpus (190)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Topological Insulators
• Topological insulators and superconductors
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Quantum Spin Hall Effect in Graphene
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• "Deconfined" quantum critical points
• Correlated quantum phenomena in the strong spin-orbit regime
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Multiple Dirac cones at the surface of the topological metal LaBi
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit gap of graphene: First-principles calculations
• Dirac materials
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Dirac Semimetals in Two Dimensions
• Topological Mott Insulators
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Heavy Fermions and Quantum Phase Transitions
• The effects of interactions on the topological classification of free fermion systems
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• 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
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Superconducting states of pure and doped graphene
• Magnetic field driven metal-insulator phase transition in planar systems
• Marginal Fermi liquid behavior from 2d Coulomb interaction
• Fermion Path Integrals And Topological Phases
• Interacting topological insulators: a review
• Quantum Criticality
• Evidence for a Gapped Spin-Liquid Ground State in a Kagome Heisenberg Antiferromagnet
• Ghost excitonic insulator transition in layered graphite
• Quantum critical transport in clean graphene
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• On the stability of U(1) spin liquids in two dimensions
• Theory of interacting electrons on the honeycomb lattice
• Properties of an algebraic spin liquid on the kagome lattice
• Non-zero temperature transport near quantum critical points
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Single valley Dirac fermions in zero-gap HgTe quantum wells
• Density waves and Cooper pairing on the honeycomb lattice
• Algebraic spin liquid as the mother of many competing orders
• Quantum critical scaling in graphene
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• Dirac, Anderson, and Goldstone on the Kagome
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Relativistic Mott criticality in graphene
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Monte-Carlo study of the semimetal-insulator phase transition in monolayer graphene with realistic inter-electron interaction potential
• Electron spectral function and algebraic spin liquid for the normal state of underdoped high $T_c$ superconductors
• Theta-terms in nonlinear sigma-models
• Nodal Liquid Theory of the Pseudo-Gap Phase of High-Tc Superconductors
• Four-loop critical exponents for the Gross-Neveu-Yukawa models
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Recent progress on correlated electron systems with strong spin-orbit coupling
• Artificial graphene with tunable interactions
• Theory of spin excitations in undoped and underdoped cuprates
• Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Emergence of supersymmetry at a critical point of a lattice model
• BCS superconductivity of Dirac electrons in graphene layers
• Interaction driven instabilities of a Dirac semi-metal
• Bootstrapping 3D Fermions
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• Gap generation and semimetal-insulator phase transition in graphene
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• The role of electron-electron interactions in two-dimensional Dirac fermions
• Fermion-induced quantum critical points
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Disorder in quantum many-body systems
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Emergence of supersymmetry on the surface of three dimensional topological insulators
• Massive Dirac fermions in single-layer graphene
• Bootstrapping 3D Fermions with Global Symmetries
• A theory of deconfined pseudo-criticality
• Is magic-angle twisted bilayer graphene near a quantum critical point?
• Quantum superconducting criticality in graphene and topological insulators
• Formation and dynamics of anti-ferromagnetic correlations in tunable optical lattices
• Anomalous thermodynamics of Coulomb interacting massless Dirac fermions in two spatial dimensions
• Solution to sign problems in half-filled spin-polarized electronic systems
• Phases of correlated spinless fermions on the honeycomb lattice
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Superconducting quantum criticality in three-dimensional Luttinger semimetals
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential
• Exotic Quantum Phase Transitions of $(2+1)d$ Dirac fermions
• Critical behavior of Dirac fermions from perturbative renormalization
• Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Emergence of supersymmetric quantum electrodynamics
• Massive fermions without fermion bilinear condensates
• Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
• Coulomb interactions at quantum Hall critical points of systems in a periodic potential
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Interaction driven phases in the honeycomb lattice from exact diagonalization
• Superconductivity of disordered Dirac fermions
• Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
• Superconducting quantum criticality of topological surface states at three loops
• Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents
• The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder
• Anomalous dimensions of scalar operators in $QE{D}_3$
• Gauge-field-assisted Kekulé quantum criticality
• Entanglement signatures of emergent Dirac fermions: kagome spin liquid & quantum criticality
• Optical conductivity of topological surface states with emergent supersymmetry
• Excitonic pairing between nodal fermions
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Dynamical Symmetry Breaking in QED_3 from the Wilson RG Point of View
• 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
• Multi-critical behavior of $Z_2\times O(2)$ Gross-Neveu-Yukawa theory in graphene
• Consistent scaling exponents at the deconfined quantum-critical point
• Designer Monte Carlo Simulation for Gross-Neveu Transition
• Neel order, quantum spin liquids and quantum criticality in two dimensions
• Dynamical Generation of Topological Masses in Dirac Fermions
• Deconfined criticality in the QED${}_3$ Gross-Neveu-Yukawa model: The $1/N$ expansion revisited
• Critical behavior of the QED${}_3$-Gross-Neveu-Yukawa model at four loops
• Instabilities on graphene's honeycomb lattice with electron-phonon interactions
• Superconductivity of disordered Dirac fermions in graphene
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• The Nambu-Jona-Lasinio Model at O(1/N^2)
• Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
• Erratum: algebraic spin liquid as the mother of many competing orders
• QED${}_3$ with quenched disorder: quantum critical states with interactions and disorder
• Interaction effects on 2D fermions with random hopping
• Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice
• Deconfined criticality from the QED${}_3$-Gross-Neveu model at three loops
• Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Mott transition in the $\pi$-flux SU($4$) Hubbard model on a square lattice
• Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor
• Two dimensional metallic phases from disordered QED${}_3$
• A strong-topological-metal material with multiple Dirac cones
• The Beta-Function of the Chiral Gross Neveu Model at O(1/N^2)
• Transition between algebraic and ${\mathbb{Z}}_2$ quantum spin liquids at large $N$
• Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class
• Attractive Hubbard Model on a Honeycomb Lattice
• Coupling, merging, and splitting Dirac points by electron-electron interaction
• Anomalous scaling of fermions and order parameter fluctuations at quantum criticality
• Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions
• Disordered fermionic quantum critical points
• Chiral tricritical point: a new universality class in Dirac systems
• Mott Transition in the Two-Dimensional Flux Phase
• Critical Casimir force in the presence of random local adsorption preference
• Fermionic multicriticality near Kekulé valence-bond ordering in honeycomb lattice
• Critical properties of the Néel/algebraic-spin-liquid transition
• Charge-Density Wave Order on a $\pi$-flux Square Lattice
• Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point
• Universal Prethermal Dynamics in Gross-Neveu-Yukawa Criticality
• Quantum phase transitions of multi-species Dirac fermions
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Emergent symmetries and coexisting orders in Dirac fermion systems
• Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics
• Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point
• Exotic pairing symmetry of interacting Dirac fermions on a $\pi$ flux lattice
• Competing orders in the Dirac-like electronic structure and the non-linear sigma model with the topological terms
• Gapless helical superconductivity on the surface of a three-dimensional topological insulator
• Effects of random potentials in three-dimensional quantum electrodynamics
• Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
• Novel criticality of Dirac fermions in the presence of emergent gauge fields
• Novel criticality of Dirac fermions from lattice symmetry breaking
• Gauged Nambu-Jona-Lasinio Model at O(1/N) with and without a Chern-Simons Term
• Nematic order on the surface of a three-dimensional topological insulator
• Scaling and Diffusion of Dirac Composite Fermions
• Critical exponents for the valence-bond-solid transition in lattice quantum electrodynamics

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• Universality in driven open quantum matter
• Order Fractionalization in a Kitaev-Kondo model
• Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
• Twisted bilayer graphene at charge neutrality: competing orders of SU(4) Dirac fermions
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling
• Twist-tuned quantum criticality in moiré bilayer graphene
• Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition
• Symmetry-breaking effects of instantons in parton gauge theories
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• SO(4) multicriticality of two-dimensional Dirac fermions
• Analog of cosmological particle production in Dirac materials
• Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Quantum-critical electrodynamics of Luttinger fermions
• Emergent soft-gap Anderson models at quantum criticality in a lattice Hamiltonian within dynamical mean field theory
• Topology-driven deconfined quantum criticality in magnetic bilayers
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Surface topological quantum criticality: Conformal manifolds and Discrete Strong Coupling Fixed Points
• Hubbard Model on the Honeycomb Lattice with an Indefinite Long-Range Interaction