Optimised Renormalisation Group Flows

Abstract

We study the optimisation of exact renormalisation group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regularisation. We consider specific optimised regulators for bosonic and fermionic fields and compare the optimised ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and non-vanishing temperature. We find that optimised flows at finite temperature factorise. This corresponds to the disentangling of thermal and quantum fluctuations. A similar factorisation is found at second order in the derivative expansion. The corresponding optimised flow for a ``proper-time renormalisation group'' is also provided to leading order in the derivative expansion.

35 pages, 3 figures, explanations and two references added, abstract streamlined, to appear in PRD

References in corpus (3)

• Exact evolution equation for the effective potential
• Mind The Gap
• Predictive power of renormalisation group flows: a comparison

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• Scaling solution for field-dependent gauge couplings in quantum gravity
• Stringballs and Planckballs for Dark Matter
• Dimensional crossover in ultracold Fermi gases from Functional Renormalisation
• Phonon Induced Instabilities in Correlated Electron Hamiltonians
• Vainshtein in the UV and a Wilsonian analysis of derivatively coupled scalars
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• Lectures in Quantum Gravity
• Four-boson bound states from a functional renormalisation group
• Weakly-interacting Bose-Bose mixtures from the functional renormalisation group
• Dark side of Weyl gravity
• On the phase structure of extra-dimensional gauge theories with fermions
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• Optimized regulator for the quantized anharmonic oscillator
• Scale symmetry breaking and generation of mass at quantum critical points
• Einstein-Heisenberg Consistency Condition Interplay with Cosmological Constant Prediction in Resummed Quantum Gravity
• Peccei-Quinn Symmetry Breaking via Asymptotically Safe Dynamical Scalegenesis: A Walking Axicolor and Axion
• Quantum-classical transition in the Caldeira-Leggett model
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics
• Renormalization and ultraviolet sensitivity of gauge vertices in universal extra dimensions
• Dense nucleonic matter and the renormalization group
• Resummed Quantum Gravity
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Quantum field theories of relativistic Luttinger fermions
• Functional renormalization group approach to color superconducting phase transition
• Renormalization of the Nonlinear O(3) Model with Theta-Term
• Anomalous criticality near semimetal-to-superfluid quantum phase transition in a two-dimensional Dirac cone model
• Quantum criticality of dipolar spin chains
• Capillary-wave models and the effective average action scheme of functional renormalization group
• Phonon renormalization and Pomeranchuk instability in the Holstein model
• Quantum interface unbinding transitions
• Non-perturbative quantum Galileon in the exact renormalization group
• Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows
• Interaction induced local moments in parallel quantum dots within the functional renormalization group approach
• Preferred foliation effects in Quantum General Relativity
• Chiral symmetry restoration in QC_2D from effective model using the functional renormalization group
• Functional renormalization group study of a four-fermion model with $CP$ violation
• Large time effective kinetics $\beta$-functions for quantum (2+p)-spin glass
• Generalized Hertz action and quantum criticality of two-dimensional Fermi systems
• Functional renormalization group study of parallel double quantum dots: Effects of asymmetric dot-lead couplings
• Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• Nonperturbative Renormalization Group for the Landau-de Gennes Model
• Prediction for the Cosmological Constant and Constraints on Susy GUTS in Resummed Quantum Gravity
• Perturbative versus Non-Perturbative Renormalization
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• A compared analysis of the susceptibility in the O(N) theory
• Functional renormalization group for signal detection and stochastic ergodicity breaking
• The $O(4)$ ${\varphi }^4$ model as an effective light meson theory: A lattice-continuum comparison
• Nonperturbative treatment of a quenched Langevin field theory
• On the Lorentz symmetry in conformally reduced Quantum Gravity
• Fermion Mass Generation without Symmetry Breaking
• Tunneling with physics-informed RG flows in the anharmonic oscillator
• Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model
• Renormalization Flow of Nonlinear Electrodynamics
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Deconfinement Phase Transition with External Magnetic Field in Friedberg-Lee Model
• Intermediate effective interactions and dynamical fermion mass generation of QCD
• Relativistic BEC extracted from a complex FRG flow equation
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• Sensitivity of Nonrenormalizable Trajectories to the Bare Scale
• An intriguing connection between Pisarski's fixed point and (2+3)-spin glasses
• Universality in the exact renormalization group: comparison to perturbation theory
• Functional renormalization group flows of $\mathcal{N}=1$ supersymmetric abelian gauge model with one chiral and one vector superfield
• IR-Improved Amplitude-Based Resummation in Quantum Field Theory: New Results and New Issues
• Superfluidity in multicomponent fermions via the functional renormalization group
• Scaling Behaviors in Active Model B+ via the Functional Renormalization Group
• Critical Exponents from Dimensional Variation
• Emergence of dynamical tensor fields in composite models of gravity
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity
• Renormalization group approach to the elastic properties of graphene bilayers
• Spin functional renormalization group for dimerized quantum spin systems
• Frequency Dependent Functional Renormalization Group for Interacting Fermionic Systems
• Backreaction of mesonic fluctuations on the axial anomaly at finite temperature
• Renormalisation of non-differentiable potentials
• One-dimensional long-range Ising model: two (almost) equivalent approximations
• Triple point in the $O(2)$ ghost model with higher-order gradient term
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• Spontaneous Symmetry Breaking without classical fields: a Functional Renormalization Group approach
• The $\theta$-vacuum from functional renormalisation
• New Approach to GUTs
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Gaussian Information Bottleneck and the Non-Perturbative Renormalization Group
• FRG analysis for a relativistic BEC in arbitrary spatial dimensions
• Multi-Regulator Functional Renormalization Group for Many-Fermion Systems
• Critical behavior of isotropic systems with strong dipole-dipole interaction from the functional renormalization group