Renormalization Group Analysis Research Articles

Marginal Fermi liquid behavior at the onset of 2kF density wave order in two-dimensional metals with flat hot spots

We analyze quantum fluctuation effects at the onset of incommensurate 2kF charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector Q connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to |kt|α with α>2. We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024

Understanding parton evolution in matter from renormalization group analysis

We perform a renormalization group (RG) analysis of collinear hadron production in deep inelastic scattering on nuclei. We consider the limit where the parent parton energy E is large, while the medium opacity L/λg remains small. We identify the fixed order and leading ln⁡(E/ξ2L) enhanced medium contributions to the semi-inclusive cross sections and derive RG equations that resum multiple emissions near the endpoints of the splitting functions at first order in opacity. These evolution equations treat the same type of radiation enhancement in matter as the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi approach, but differ in the way one regulates the collinear divergences. They provide a unique analytic insight into the problem of resummation and a faster and more efficient path to phenomenology. The new RG evolution framework is applied to study fragmentation in eA reactions.

In and Out of Criticality? State-Dependent Scaling in the Rat Visual Cortex

The presumed proximity to a critical point is believed to endow the brain with scale-invariant statistics, which are thought to confer various functional advantages in terms of its information processing, storage, and transmission capabilities. To assess the relationship between scaling and cortical states, we apply a phenomenological renormalization group analysis to 3-h spiking data recordings from the urethane-anesthetized rat's visual cortex. Under this type of anesthesia, cortical states dynamically shift across a spectrum of synchronization levels, defined by population spiking rate variability. By developing a scaling criterion based on the kurtosis of the momentum-space activity distribution, our study combines the coarse-graining method with state-dependent analysis. We find that scaling signatures only appear as spiking variability surpasses a specified threshold. Notably, within this regime, scaling exponents show relative stability. Conversely, subthreshold activity is primarily asynchronous and fails to meet the scaling criterion. Our results suggest that a wide range of cortical states corresponds to small deviations around a critical point, with the system fluctuating in and out of criticality, spending roughly three-quarters of the experiment duration within a scaling regime. Published by the American Physical Society 2024

Crossover from ordinary to higher order Van Hove singularity in a honeycomb system: A parquet renormalization group analysis

Crossover from ordinary to higher order Van Hove singularity in a honeycomb system: A parquet renormalization group analysis

Measurement-Induced Phase Transition for Free Fermions above One Dimension.

A theory of the measurement-induced entanglement phase transition for free-fermion models in d>1 dimensions is developed. The critical point separates a gapless phase with ℓ^{d-1}lnℓ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with ℓ^{d-1} scaling, where ℓ is a size of the subsystem. The problem is mapped onto an SU(R) replica nonlinear sigma model in d+1 dimensions, with R→1. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for d=1+ε with ε≪1. Further, we carry out a numerical study of the transition for a d=2 model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, ν≈1.4.

Non-Hermitian Strongly Interacting Dirac Fermions.

Exotic quantum phases and phase transition in the strongly interacting Dirac systems have attracted tremendous interests. On the other hand, non-Hermitian physics, usually associated with dissipation arising from the coupling to environment, emerges as a frontier of modern physics in recent years. In this Letter, we investigate the interplay between non-Hermitian physics and strong correlation in Dirac-fermion systems. We generalize the projector quantum Monte-Carlo (PQMC) algorithm to the non-Hermitian interacting fermionic systems. Employing PQMC simulation, we decipher the ground-state phase diagram of the honeycomb Hubbard model with spin resolved non-Hermitian asymmetric hopping processes. The antiferromagnetic (AFM) ordering induced by Hubbard interaction is enhanced by the non-Hermitian asymmetric hopping. Combining PQMC simulation and renormalization group analysis, we reveal that the quantum phase transition between Dirac semi-metal and AFM phases belongs to Hermitian chiral XY universality class, implying that a Hermitian Gross-Neveu transition is emergent at the quantum critical point although the model is non-Hermitian.

Flipped SU(5): unification, proton decay, fermion masses and gravitational waves

We study supersymmetric (SUSY) flipped SU(5) × U(1) unification, focussing on its predictions for proton decay, fermion masses and gravitational waves. We performed a two-loop renormalisation group analysis and showed that the SUSY flipped SU(5) model predicts a high GUT scale MGUT> 1016 GeV. We also investigated the restrictions on the MB−L scale which is associated with the U(1)χ breaking scale. We found that the MB−L scale can vary in a broad region with negligible or little effect on the value of MGUT. Proton decay in this model is induced by dimension-6 operators only. The dimension-5 operator induced by SUSY contribution is suppressed due to the missing partner mechanism. We found that the partial decay width p → π0e+ is high suppressed, being at least one order of magnitude lower than the future Hyper-K sensitivity. We also studied fermion (including neutrino) masses and mixings which can also influence proton decay. We presented two scenarios of flavour textures to check the consistency of the results with fermion masses and mixing. The B − L gauge breaking leads to the generation of cosmic strings. The B − L scale here is not constrained by gauge coupling unification. If this scale is very close that of GUT breaking, strings can be unstable due to the decay to monopole-antimonople pair. Such metastable strings can be used to explain the NANOGrav signals of stochastic gravitational wave background, which may be interpreted here as resulting from the decay of metastable cosmic strings.

A tensor renormalization group analysis of an evolutionary game of competing Ising and Potts subgames

The temperature-induced phase transitions of an evolutionary game of competing Ising- and Potts-type coordination subgames are studied using the tensor renormalization group method proposed by Michael Levin and Cody P. Nave. Depending on the relative strength of the subgames, a continuous Ising order to disorder or a continuous Potts order to disorder or consecutive first-order Potts order to Ising order and continuous Ising order to disorder phase transitions are observed. In the game-theoretic interpretation of the model, these results imply that while both types of coordination can spread in the population at low noise levels, one of them will always be dominant in equilibrium. Under a relatively narrow set of circumstances, a small increase in noise can cause the population to suddenly switch from Ising-type coordination to Potts-type coordination. The results are in general qualitative and quantitative agreement with previous Monte Carlo simulation findings.

Two-Pomeron Interaction

We study the interaction of two discrete pomeron fields while considering mass mixing and the general structure of the interaction potential for pomerons within the framework for a functional renormalization group analysis of Reggeon field theory. We find fixed points from the zeros of the beta function establishing the existence of three groups of solutions: the first corresponds to two uncoupled pomerons, the second is a solution known as a “pomeron–odderon” interaction, and the final is a real general solution with an interaction potential. We also study its universal properties around this fixed point. This analysis allows for a discussion for the first time on the mixing of two pomerons through renormalization flow paths from the ultraviolet to the non-perturbative infrared regions. Finally, we comment on its role in high-energy scattering.

The breaking of Mermin-Wagner-Hohenberg's theorem for fractional systems

The Mermin-Wagner-Hohenberg theorem forbids the existence of long range order in two dimensional systems, since continuous symmetries cannot be spontaneously broken in d≤2. However, one of the premises for the validity of the theorem is that the energy-momentum dispersion of the quanta responsible for the order parameter fluctuations has a quadratic form, ε(k)=Ak2. In this paper we address the emergence of a fractional order energy-momentum dispersion in d-dimensional systems, leading to important consequences for the existence of long-range order in the case d=2. A first order renormalization group analysis in the ϵ-expansion is also performed in the fractional regime. It is shown that for fractional systems the universality classes are characterized by the number of spatial dimensions d and the number of components n of the order parameter, as in the case of integer order systems, but the labeling by the fractional order α is also required.

Robust topological superconductivity in spin–orbit coupled systems at higher-order van Hove filling

Van Hove singularities in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin–orbit coupling can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between van Hove singularities (VHSs) and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle–particle and particle-hole channels associated with higher-order VHSs, we find that the chiral p±ip pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong spin–orbit coupling (SOC) and offers fresh insights into the exploration of topological superconductivity.

Dynamic renormalization group analysis of the chiral smectic-C to smectic-C phase transition

The chiral smectic-C to smectic-C (SmC -SmC) phase transition has been studied using dynamic renormalization group (DRG) analysis. Langevin equations are derived from the nonlinear elastic model of the SmC -SmC phase transition. The DRG equations are derived. The DRG analysis predicts the Kosterlitz-Thouless transition at low frequency limit and Kardar-Parisi-Zhang (KPZ) fixed point. The DRG calculation confirms that the SmC -SmC phase transition belong to the KPZ universality class.

A tensor renormalization group analysis of the Blume–Capel model inspired by game theory

After showing that it can be parametrized as the elementary coordination game of evolutionary game theory, this paper analyzes the Blume–Capel model using the tensor renormalization group method introduced by Michael Levin and Cody P. Nave. The results obtained along the cross sections defined by the coordination game parametrization expand and corroborate earlier findings regarding the location, order, and critical properties of the order–disorder phase transitions in both the zero-field and non-zero-field versions of the Blume–Capel model.

A plane defect in the 3d O(N) model

It was recently found that the classical 3d O(N)(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as \langle \vec{S}(x) \cdot \vec{S}(0)\rangle \sim \frac{1}{(\log x)^q}〈S→(x)⋅S→(0)⟩∼1(logx)q. This universality class exists for a range 2 ≤N <N_c2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate N_c > 3Nc>3. In this work, we extend this result to the 3d O(N)(N) model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite N ≥2N≥2. We additionally show, in agreement with our RG analysis, that the line of defect fixed points which is present at N = ∞N=∞ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N1/N corrections. We study the “central charge” aa for the O(N)O(N) model in the boundary and interface geometries and provide a non-trivial detailed check of an aa-theorem by Jensen and O’Bannon. Finally, we revisit the problem of the O(N)(N) model in the semi-infinite geometry. We find evidence that at N = N_cN=Nc the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for N > N_cN>Nc.

On the renormalization of non-polynomial field theories

A class of scalar models with non-polynomial interaction, which naturally admits an analytical resummation of the series of tadpole diagrams is studied in perturbation theory. In particular, we focus on a model containing only one renormalizable coupling that appear as a multiplicative coefficient of the squared field. A renormalization group analysis of the Green functions of the model shows that these are only approximated solutions of the flow equations, with errors proportional to powers of the coupling, therefore smaller in the region of weak coupling. The final output of the perturbative analysis is that the renormalized model is non-interacting with finite mass and vanishing vertices or, in an effective theory limited by an ultraviolet cut-off, the vertices are suppressed by powers of the inverse cut-off. The relation with some non-polynomial interactions derived long ago, as solutions of the linearized functional renormalization group flow equations, is also discussed.

Renormalization group analysis of a self-organized critical system: intrinsic anisotropy vs random environment

Abstract We study a self-organized critical system coupled to an isotropic random fluid environment. The former is described by a strongly anisotropic continuous (coarse-grained) model introduced by Hwa and Kardar (1989 Phys. Rev. Lett. 62 1813; 1992 Phys. Rev. A 45 7002); the latter is described by the stirred Navier–Stokes equation due to Forster et al (1977 Phys. Rev. A 16 732). The full problem of two coupled stochastic equations is represented as a field-theoretic model, which is shown to be multiplicatively renormalizable. The corresponding renormalization group (RG) equations possess a semi-infinite curve of fixed points in the four-dimensional space of the model parameters. The whole curve is infrared attractive for realistic values of parameters; its endpoint corresponds to the purely isotropic regime where the original Hwa–Kardar nonlinearity becomes irrelevant. There, one is left with a simple advection of a passive scalar field by the external environment. The main critical dimensions are calculated to leading (one-loop) order (first terms in the ϵ = 4 − d expansion); some of them are exact in all orders. These dimensions remain the same along that curve, which makes it reasonable to interpret it as a single universality class. However, the correction exponents do vary along the curve. It is therefore not clear whether the curve survives in all orders of the RG expansion or shrinks to a single point when the higher-order corrections are taken into account.

Field-Theoretic Renormalization Group in Models of Growth Processes, Surface Roughening and Non-Linear Diffusion in Random Environment: Mobilis in Mobili

This paper is concerned with intriguing possibilities for non-conventional critical behavior that arise when a nearly critical strongly non-equilibrium system is subjected to chaotic or turbulent motion of the environment. We briefly explain the connection between the critical behavior theory and the quantum field theory that allows the application of the powerful methods of the latter to the study of stochastic systems. Then, we use the results of our recent research to illustrate several interesting effects of turbulent environment on the non-equilibrium critical behavior. Specifically, we couple the Kazantsev–Kraichnan “rapid-change” velocity ensemble that describes the environment to the three different stochastic models: the Kardar–Parisi–Zhang equation with time-independent random noise for randomly growing surface, the Hwa–Kardar model of a “running sandpile” and the generalized Pavlik model of non-linear diffusion with infinite number of coupling constants. Using field-theoretic renormalization group analysis, we show that the effect can be quite significant leading to the emergence of induced non-linearity or making the original anisotropic scaling appear only through certain “dimensional transmutation”.

The Variational Problem and Background Field in the Renormalization Group Method for Nonlinear Sigma Models

We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in d=3,4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d = 3, 4$$\\end{document} and adapt it to a class of nonlinear sigma models in d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}. The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis.

Quantitative bounds on vortex fluctuations in 2d$2d$ Coulomb gas and maximum of the integer‐valued Gaussian free field

AbstractIn this paper, we study the influence of the vortices on the fluctuations of systems such as the Coulomb gas, the Villain model, or the integer‐valued Gaussian free field (GFF). In the case of the Villain model, we prove that the fluctuations induced by the vortices are at least of the same order of magnitude as the ones produced by the spin wave. We obtain the following quantitative upper bound on the two‐point correlation in when The proof is entirely nonperturbative. Furthermore, it provides a new and algorithmically efficient way of sampling the Coulomb gas. For the Coulomb gas, we obtain the following lower bound on its fluctuations at high inverse temperature: This estimate coincides with the predictions based on Renormalization group (RG) analysis by José et al. [Phys. Rev. B 16 (1977), no. 3, 1217] and suggests that the Coulomb potential at inverse temperature should scale like a GFF of inverse temperature of order .Finally, we transfer the above vortex fluctuations via a duality identity to the integer‐valued GFF by showing that its maximum deviates in a quantitative way from the maximum of a usual GFF. More precisely, we show that with high probability when where is an integer‐valued GFF in the box at inverse temperature . Applications to the free energies of the Coulomb gas, the Villain model, and the integer‐valued GFF are also considered.

Field-theoretic analysis of directed percolation: Three-loop approximation.

The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we study this model by means of the field-theoretic formulation with a subsequent renormalization group analysis. We calculate all critical exponents needed for the quantitative description of the corresponding universality class to the third order in perturbation theory. Using dimensional regularization with minimal subtraction scheme, we carry out perturbative calculations in a formally small parameter ɛ, where ɛ=4-d is a deviation from the upper critical dimension d_{c}=4. We use a nontrivial combination of analytical and numerical tools in order to determine ultraviolet divergent parts of Feynman diagrams.