Critical behavior of the (2+1)-dimensional Thirring model

Abstract

We investigate chiral symmetry breaking in the (2+1)-dimensional Thirring model as a function of the coupling as well as the Dirac flavor number Nf with the aid of the functional renormalization group. For small enough flavor number Nf < Nfc, the model exhibits a chiral quantum phase transition for sufficiently large coupling. We compute the critical exponents of this second order transition as well as the fermionic and bosonic mass spectrum inside the broken phase within a next-to-leading order derivative expansion. We also determine the quantum critical behavior of the many-flavor transition which arises due to a competition between vector and chiral-scalar channel and which is of second order as well. Due to the problem of competing channels, our results rely crucially on the RG technique of dynamical bosonization. For the critical flavor number, we find Nfc ~ 5.1 with an estimated systematic error of approximately one flavor.

arXiv comment28 pages, 14 figures

References in corpus (83)

• Electric Field Effect in Atomically Thin Carbon Films
• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Exactly massless quarks on the lattice
• A Method for Simulating Chiral Fermions on the Lattice
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• Chiral Fermions from Lattice Boundaries
• Functional renormalization group approach to correlated fermion systems
• Axial symmetries in lattice QCD with Kaplan fermions
• Interactions and phase transitions on graphene's honeycomb lattice
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Walking in the SU(N)
• Is graphene in vacuum an insulator?
• Conformality Lost
• Theory of interacting electrons on the honeycomb lattice
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Lectures on the functional renormalization group method
• Conformal Phase Transition in Gauge Theories
• QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via "algebraic" Fermi liquid
• The Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories
• Algebraic Fermi liquid from phase fluctuations: "topological" fermions, vortex "berryons" and QED3 theory of cuprate superconductors
• Renormalization Flow of Bound States
• Critical exponents from optimised renormalisation group flows
• The Physical Spectrum of Conformal SU(N) Gauge Theories
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• QED3 theory of underdoped high temperature superconductors
• Flow Equations and BRS Invariance for Yang-Mills Theories
• Chiral phase structure of QCD with many flavors
• Effective Action for the Quark-Meson Model
• Chiral phase boundary of QCD at finite temperature
• The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3
• A new method to solve the Non Perturbative Renormalization Group equations
• Quantum Critical Behaviour in a Graphene-like Model
• Antiferromagnetism from phase disordering of a d-wave superconductor
• Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$
• Asymptotic safety: a simple example
• Ising exponents from the functional renormalisation group
• Exact flow equation for composite operators
• Computation of Critical Exponent ηat O(1/N^3) in the Four Fermi Model in Arbitrary Dimensions
• Catalysis of Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• Renormalization group flows into phases with broken symmetry
• Phase transition and critical behaviour of the d=3 Gross-Neveu model
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene
• Non-Compact QED_3 with N_f=1 and N_f=4
• Critical exponents of the Gross-Neveu model from the effective average action
• Non-compact QED_3 with N_f >=2
• Phase structure of lattice QCD for general number of flavors
• Flow Equations without Mean Field Ambiguity
• Spontaneously Broken Lorentz Invariance in Three-Dimensional Gauge Theories
• Gauge invariance of a critical number of flavours in QED3
• UV fixed-point structure of the three-dimensional Thirring model
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Beyond Miransky Scaling
• Fermion bags, duality and the three dimensional massless lattice Thirring model
• Geometrical and topological aspects of graphene and related materials
• Critical Flavor Number in the Three Dimensional Thirring Model
• The Three Dimensional Thirring Model for Small N_f
• Effective theory of high-temperature superconductors
• Scaling laws near the conformal window of many-flavor QCD
• Dynamical Symmetry Breaking in QED_3 from the Wilson RG Point of View
• Spinors in euclidean field theory, complex structures and discrete symmetries
• Infrared cutoff dependence of the critical flavor number in three-dimensional QED
• Thirring Model as a Gauge Theory
• Meson masses in large Nf QCD from the Bethe-Salpeter equation
• O(1/N_f) Corrections to the Thirring Model in 2<d<4
• Large-N analysis of (2+1)-dimensional Thirring model
• Modified Fermi-sphere, pairing gap and critical temperature for the BCS-BEC crossover
• Spontaneous Breakdown of the Lorentz Invariance
• Thirring Model as a Gauge Theory
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• The Phase Diagram of the Three Dimensional Thirring Model
• The Three Dimensional Thirring Model for N_f=4 and N_f=6
• Effective Action and Conformal Phase Transition in Three-Dimensional QED
• Fermion Mass Generation in the D-dimensional Thirring Model as a Gauge Theory
• Spontaneous symmetry breaking in the colored Hubbard model
• Spontaneous Magnetization in Lorentz Invariant Theories
• Dynamical chiral symmetry breaking in QED${}_3$ at finite density and impurity potential
• Effects of flavor-symmetry violation from staggered fermion lattice simulations of graphene
• Strongly coupled lattice gauge theory with dynamical fermion mass generation in three dimensions
• Spontaneous Lorentz Symmetry Breaking by Anti-Symmetric Tensor Field

Cited by in corpus (60)

• The nonperturbative functional renormalization group and its applications
• Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
• RG Flows and Bifurcations
• On the Phase Structure of Many-Flavor QED${}_3$
• Quantum critical behavior in three dimensional lattice Gross-Neveu models
• Solution to sign problems in half-filled spin-polarized electronic systems
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Phase diagram of electronic systems with quadratic Fermi nodes in $2<d<4$: $2+\epsilon$ expansion, $4-\epsilon$ expansion, and functional renormalization group
• 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
• Solving functional flow equations with pseudo-spectral methods
• Multi-meson Yukawa interactions at criticality
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Multicritical behavior in models with two competing order parameters
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• Fermi velocity renormalization and dynamical gap generation in graphene
• Fermion-induced quantum criticality with two length scales in Dirac systems
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization
• Bootstrapping $N_f=4$ conformal QED${}_3$
• DoFun 3.0: Functional equations in Mathematica
• Compatible orders and fermion-induced emergent symmetry in Dirac systems
• Critical flavour number of the Thirring model in three dimensions
• Quantum criticality of reconstructing Fermi surfaces in antiferromagnetic metals
• Spontaneous breaking of Lorentz symmetry in $(2+\epsilon )$-dimensional QED
• On the Critical Flavor Number in the 2+1$d$ Thirring Model
• Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Fractionalized quantum criticality in spin-orbital liquids from field theory beyond the leading order
• Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions
• Momentum dependence of quantum critical Dirac systems
• Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1d
• Local potential approximation for the renormalization group flow of fermionic field theories
• Gross-Neveu-Heisenberg criticality from competing nematic and antiferromagnetic orders in bilayer graphene
• Emergent symmetries and coexisting orders in Dirac fermion systems
• From Domain Wall to Overlap in 2+1d
• Conformality and self-duality of $N_f=2$ QED${}_3$
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Symmetries of Thirring models on 3d lattices
• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Space of non-Fermi liquids
• SO(4) multicriticality of two-dimensional Dirac fermions
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• The relevance of the three dimensional Thirring coupling at finite temperature and density
• Bosonization of the Thirring Model in 2+1 Dimensions
• Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Excitonic gap generation in thin-film topological insulators
• Dirac quantum criticality in twisted double bilayer transition metal dichalcogenides
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions
• Renormalization of the optical band gap through an effective Thirring interaction for massive Dirac-like electrons
• Four-Fermion Theories with Exact Chiral Symmetry in Three Dimensions
• Higher-Dimensional Chirally Stabilized Fixed Points and Their Deformations