Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group

Abstract

Using the nonperturbative renormalization group, we study the existence of bound states in the symmetry-broken phase of the scalar ${\varphi }^4$ theory in all dimensions between two and four and as a function of the temperature. The accurate description of the momentum dependence of the two-point function, required to get the spectrum of the theory, is provided by means of the Blaizot--Méndez-Galain--Wschebor approximation scheme. We confirm the existence of a bound state in dimension three, with a mass within 1% of previous Monte-Carlo and numerical diagonalization values.

arXiv comment8 pages, 4 figures

References in corpus (54)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Critical Exponents of the N-vector model
• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• Solving the 3D Ising Model with the Conformal Bootstrap
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bootstrapping the O(N) Vector Models
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• Critical Exponents from the Effective Average Action
• Derivative Expansion of the Exact Renormalization Group
• The critical exponents of the superfluid transition in He4
• Nonperturbative renormalization group approach to frustrated magnets
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Interaction induced delocalisation for two particles in a periodic potential
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Pairing of Cooper Pairs in a Fully Frustrated Josephson Junction Chain
• Magnetic excitation spectrum of dimerized antiferromagnetic chains
• A new method to solve the Non Perturbative Renormalization Group equations
• Conformal Field Theories in Fractional Dimensions
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Observation of two-magnon bound states in the two-leg ladders of (Ca,La)14Cu24O41
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation
• Fractional and Integer Excitations in Quantum Antiferromagnetic Spin 1/2 Ladders
• Solutions of renormalization group flow equations with full momentum dependence
• Strong-Coupling Expansions for Multiparticle Excitations: Continuum and Bound States
• Non-perturbative fixed point in a non-equilibrium phase transition
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• Linked Cluster Series Expansions for Two-Particle Bound States
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Analytic continuation by averaging Padé approximants
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model
• Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking
• Nonperturbative renormalization-group approach to strongly-correlated lattice bosons
• Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point
• Flow equations for spectral functions at finite external momenta
• Confinement vs Deconfinement of Cooper Pairs in One-Dimensional Spin-3/2 Fermionic Cold Atoms
• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• The Spectrum of the 2+1 Dimensional Gauge Ising Model
• Non-perturbative states in the 3D phi^4 theory
• Bound states and glueballs in three-dimensional Ising systems
• Neutral Bound States in Kink-like Theories
• On the 2-point function of the O(N) model
• Bound states in the three dimensional phi^4 model
• Spectral Functions from the Functional Renormalization Group
• Universal critical behavior of the two-magnon-bound-state mass gap for the (2+1)-dimensional Ising model

Cited by in corpus (23)

• The nonperturbative functional renormalization group and its applications
• Spectral functions in the ${\varphi }^4$-theory from the spectral DSE
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• A Conjecture on the Minimal Size of Bound States
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• The ordered phase of $O(N)$ model within the Non-Perturbative Renormalization Group
• Persistent oscillations after quantum quenches in $d$ dimensions
• Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions
• Superuniversal transport near a $(2+1)$-dimensional quantum critical point
• Bound states in Functional Renormalization Group
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Harmonic expansion of the effective potential in Functional Renormalization Group at finite chemical potential
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Determining wave equations in holographic QCD from Wilsonian renormalization group
• Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency
• Interacting two-particle states in the symmetric phase of the chiral Nambu--Jona-Lasinio model
• Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps
• Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions
• Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas
• Quantum quenches with long range interactions