Renormalization Group Analysis Research Articles

Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids.

We investigate the nature of the topological quantum phase transition between the gapless and gapped Kitaev quantum spin liquid phases away from the exactly solvable point. The transition is driven by anisotropy of the Kitaev couplings. At the critical point, the two Dirac points of the gapless Majorana modes merge, resulting in the formation of a semi-Dirac point with quadratic and linear band touching directions. We derive an effective Gross-Neveu-Yukawa-type field theory that describes the topological phase transition in the presence of additional magnetic interactions. We obtain the infrared scaling form of the propagator of the dynamical Ising order parameter field and perform a renormalization-group analysis. The universality of the transition is found to be different from that of symmetry-breaking phase transitions of semi-Dirac electrons. However, as in the electronic case, the Majorana fermions acquire an anomalous dimension, indicative of the breakdown of the fractionalized quasiparticle description.

The role of mobility in epidemics near criticality

Abstract The general epidemic process (GEP), also known as susceptible-infected-recovered model, provides a minimal model of how an epidemic spreads within a population of susceptible individuals who acquire permanent immunization upon recovery. This model exhibits a second-order absorbing state phase transition, commonly studied assuming immobile healthy individuals. We investigate the impact of mobility on the scaling properties of disease spreading near the extinction threshold by introducing two generalizations of GEP, where the mobility of susceptible and recovered individuals is examined independently. In both cases, including mobility violates GEP’s rapidity reversal symmetry and alters the number of absorbing states. The critical dynamics of the models are analyzed through a perturbative renormalization group (RG) approach and large-scale stochastic simulations using a Gillespie algorithm. The RG analysis predicts both models to belong to the same novel universality class describing the critical dynamics of epidemic spreading when the infected individuals interact with a diffusive species and gain immunization upon recovery. At the associated RG fixed point, the immobile species decouples from the dynamics of the infected species, dominated by the coupling with the diffusive species. Numerical simulations in two dimensions affirm our RG results by identifying the same set of critical exponents for both models. Violation of the rapidity reversal symmetry is confirmed by breaking the associated hyperscaling relation. Our study underscores the significance of mobility in shaping population spreading dynamics near the extinction threshold.

Universality in the 2d Quasi-periodic Ising Model and Harris–Luck Irrelevance

We prove that in the 2D Ising model with a weak bidimensional quasi-periodic disorder in the interaction, the critical behavior is the same as in the non-disordered case; that is, the critical exponents for the specific heat and energy-energy correlations are identical, and no logarithmic corrections are present. The disorder produces a quasi-periodic modulation of the amplitude of the correlations and a renormalization of the velocities, that is, the coefficients of the rescaling of positions, and of the critical temperature. The result establishes the validity of the prediction based on the Harris–Luck criterion, and it provides the first rigorous proof of universality in the Ising model in the presence of quasi-periodic disorder in both directions and for any angle. Small divisors are controlled assuming a Diophantine condition on the frequencies, and the convergence of the series is proved by Renormalization Group analysis.

Disordered non-Fermi liquid fixed point for two-dimensional metals at Ising-nematic quantum critical points

Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point”. Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron’s density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.

Renormalization group analysis of the Anderson model on random regular graphs

We present a renormalization group (RG) analysis of the problem of Anderson localization on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The RG equations necessarily involve two parameters (one being the changing connectivity of subtrees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the nonmonotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence. Our theory provides a simple and coherent explanation for the unusual scaling behavior observed in numerical data of the Anderson model on RRG and of many-body localization.

Systematic compactification of the two-channel Kondo model. III. Extended field-theoretic renormalization group analysis

Systematic compactification of the two-channel Kondo model. III. Extended field-theoretic renormalization group analysis

Electron–electron interactions in partially mixed helical states

We theoretically study the effect of electron–electron interactions in one-dimensional partially mixed helical states. These helical states can be realized at the edges of two-dimensional topological insulators with partially broken time-reversal symmetry, resulting in helical gapped states. Using the bosonization method and renormalization group analysis, we identify weak gap, crossover, and strong gap regimes in the phase diagram. We find that strong electron–electron interaction mixes the helicity of the states, leading to the relevant strong gap regime. We investigate the charge and spin density wave correlation functions in different relevancy regimes of the gap mediated by interactions, where in the case of strong repulsive interaction, the spin density wave dominates the charge density wave. Additionally, employing the Memory function technique, we calculate the effect of mixed helicity on the charge transport in a sufficiently long edge. We find a non-uniform temperature dependence for the charge conductivity in both the strong and weak gap regimes with distinct features.

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

Percolation transition for random forests in d⩾3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$d\\geqslant 3$\\end{document}

The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor β>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\beta >0$\\end{document} per edge. It arises as the q→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$q\ o 0$\\end{document} limit of the q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$q$\\end{document}-state random cluster model with p=βq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$p=\\beta q$\\end{document}. We prove that in dimensions d⩾3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$d\\geqslant 3$\\end{document} the arboreal gas undergoes a percolation phase transition. This contrasts with the case of 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} where no percolation transition occurs.The starting point for our analysis is an exact relationship between the arboreal gas and a non-linear sigma model with target space the fermionic hyperbolic plane H0|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{H}^{0|2}$\\end{document}. This latter model can be thought of as the 0-state Potts model, with the arboreal gas being its random cluster representation. Unlike the standard Potts models, the H0|2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{H}^{0|2}$\\end{document} model has continuous symmetries. By combining a renormalisation group analysis with Ward identities we prove that this symmetry is spontaneously broken at low temperatures. In terms of the arboreal gas, this symmetry breaking translates into the existence of infinite trees in the thermodynamic limit. Our analysis also establishes massless free field correlations at low temperatures and the existence of a macroscopic tree on finite tori.

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

Quadratic gravity in analogy to quantum chromodynamics: Light fermions in its landscape

We investigate a nonperturbative approach to quantum gravity built in terms of analogies between quadratic gravity and quantum chromodynamics. This approach is based on a conjectured phase transition between quadratic gravity in the trans-Planckian regime and an effective field theory, with general relativity as the leading-order term, below the Planck scale. We point out that not all aspects of the analogy between quadratic gravity and quantum chromodynamics are desired. A possible mechanism of chiral symmetry breaking driven by quantum gravity fluctuations could make this setup incompatible with our observed Universe. Here, we put forward a first investigation of chiral symmetry breaking in the context of quadratic gravity. We find indication that gravity, despite being an attractive force, does not trigger chiral symmetry breaking in a nonperturbative regime. This result is based on a (functional) renormalization group analysis of four-fermion interactions coupled to quadratic gravity. We also comment on the particularities associated with the single-flavor case. In summary, the analogy between quadratic gravity and chromodynamics passes this first phenomenological viability test. Published by the American Physical Society 2024

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.

Standard model Higgs inflation supplemented by minimal dark matter

Renormalization group analysis with the present measurements of the top quark mass mt=172.69±0.30 GeV [1] indicates that the Standard Model (SM) Higgs potential becomes unstable at energy scales ∼1010 GeV. This may be interpreted as hinting at new particles at high energy. The minimal extension of the SM that can avoid this instability while leaving the SM Higgs as the sole scalar particle of the theory is obtained by adding suitable fermions to the SM. These fermions are good dark matter candidates and the model is known as the minimal dark matter model. We revisit the inflationary scenario based on the minimal dark matter model, taking into account updated parameter constraints and recent understanding of reheating dynamics. We explore the model with different values of the right-handed neutrino mass and find that the cosmological prediction is insensitive to such details. We obtained a spectral index of the cosmic microwave background ns=0.9672 and a tensor-to-scalar ratio r=0.0031 as a robust prediction of this scenario. Published by the American Physical Society 2024

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.