Nonanalytic Terms Research Articles

Chiral analysis of the nucleon mass and sigma commutator

Schemes for describing the light quark mass dependence of the nucleon mass calculated in lattice QCD are compared. The three schemes in consideration include a fully relativistic and Lorentz covariant scheme, one that is fully relativistic but not Lorentz covariant, and a semirelativistic scheme utilizing the heavy baryon approximation. Calculations of observables involving pseudoscalar meson loop diagrams generate nonanalytic terms proportional to square roots and logarithms of the quark mass. The three schemes all yield the correct model-independent leading and next-to-leading nonanalytic terms of the chiral expansion of the baryon mass. Results for the masses of the other members of the octet are also presented. Here, low-energy coefficients of the analytic terms of the expansion for the nucleon and hyperons are constrained by lattice QCD results and are demonstrated to be independent of the renormalization scheme used. The differences in the leading coefficient of the chiral expansions are found to be consistent with strange quark counting. Using the schemes examined herein, we report results for the pion-nucleon sigma commutator based upon recent lattice results from the CLS Collaboration. We find σπN=51.7±3.2±1.4 MeV, where the uncertainties are statistical and systematic, respectively. Published by the American Physical Society 2024

Mode recombination formula and nonanalytic term in an effective potential at finite temperature on a compactified space

We develop a new formula called a mode recombination formula, and we can recast the effective potential at finite temperature in one-loop approximation for fermion and scalar fields on the D-dimensional spacetime, Sτ1×RD−(p+1)×∏i=1pSi1 into a convenient form for discussing nonanalytic terms, which cannot be written in the form of any positive integer power of the field-dependent mass squared, in the effective potential. The formula holds irrespective of whether the field is a fermion or a scalar and of boundary conditions for spatial Si1 directions and clarifies the importance of zero modes in the Matsubara and Kaluza-Klein modes for the existence of the nonanalytic terms. The effective potential is drastically simplified further to obtain the nonanalytic terms in easier and more transparent way. In addition to reproducing previous results, we find that there exists no nonanalytic term for the fermion field with arbitrary boundary condition for the spatial Si1 direction, which is also the case for the scalar field with the antiperiodic boundary condition for the spatial direction. Published by the American Physical Society 2024

Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

Cosmological perturbation theory is known to converge poorly for predicting the spherical collapse and void evolution of collisionless matter. Using the exact parametric solution as a testing ground, we develop two asymptotic methods in spherical symmetry that resolve the gravitational evolution to much higher accuracy than Lagrangian perturbation theory (LPT), which is the current gold standard in the literature. One of the methods selects a stable fixed-point solution of the renormalization-group flow equation, thereby predicting already at the leading order the critical exponent of the phase transition to collapsed structures. The other method completes the truncated LPT series far into the UV regime, by adding a non-analytic term that captures the critical nature of the gravitational collapse. We find that the UV method most accurately resolves the evolution of the nonlinear density as well as its one-point probability distribution function. Similarly accurate predictions are achieved with the renormalization-group method, especially when paired with Pad\'e approximants. Further, our results yield new, very accurate, formulas to relate linear and nonlinear density contrasts. Finally, we chart possible ways on how to adapt our methods to the case of cosmological random field initial conditions.

Nonanalytic term in the effective potential at finite temperature for a scalar field on compactified space

We study non-analytic terms, which cannot be written in the form of any positive integer power of field-dependent mass squared, in effective potential at finite temperature in one-loop approximation for a real scalar field on the $D$-dimensional space-time, $S_{\tau}^1\times R^{D-(p+1)}\times\prod_{i=1}^pS_i^1$. The effective potential can be recast into the integral form in the complex plane by using the integral representation for the modified Bessel function of the second kind and the analytical extension for multiple mode summations. The pole structure of the mode summations is clarified and all the non-analytic terms are obtained by the residue theorem. We find that the effective potential has a non-analytic term when the dimension of the flat Euclidean space, $D-(p+1)$ is odd. There appears only one non-analytic term for the given values of $D$ and $p$, for which the non-analytic term exists.

Role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice -- such as $(p_{x},\,p_{y})$-wave and $(d_{x^{2}-y^{2}},\,d_{xy})$-wave. Such a system has two possible superconducting states: the chiral state (e.g. $p+ip$ or $d+id$), which breaks time-reversal symmetry, and the nematic state (e.g. $p+p$ or $d+d$), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A non-analytic cubic term arises, as in the case of a conventional $s$-wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. We analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.

Confined vortex surface and irreversibility. 1. Properties of exact solution

We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (Migdal, 2021). These surfaces avoid the Kelvin–Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only in an exceptional case considered long ago by Burgers and Townsend, where it decays as a Gaussian on both sides of the sheet. In generic asymmetric vortex sheets (Shariff, 2021), vorticity leaks to one side or another, making such sheets inadequate for vortex sheet statistics and anomalous dissipation. We conjecture that the vorticity in a turbulent flow collapses on a special kind of surface (confined vortex surface or CVS), satisfying some equations involving the tangent components of the local strain tensor. The most important qualitative observation is that the inequality needed for this solution’s stability breaks the Euler dynamics’ time reversibility. We interpret this as dynamic irreversibility. We have also represented the enstrophy as a surface integral, conserved in the Navier–Stokes equation in the turbulent limit, with vortex stretching and viscous diffusion terms exactly canceling each other on the CVS surfaces. We have studied the CVS equations for the cylindrical vortex surface for an arbitrary constant background strain with two different eigenvalues. This equation reduces to a particular version of the stationary Birkhoff–Rott equation for the 2D flow with an extra nonanalytic term. We study some general properties of this equation and reduce its solution to a fixed point of a map on a sphere, guaranteed to exist by the Brouwer theorem.

Mathcal{N} = 4 supersymmetric Yang-Mills thermodynamics to order \u03bb2

We calculate the resummed perturbative free energy of mathcal{N} = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM4,4 ring diagrams. Non-analytic terms at mathcal{O} (λ3/2) and mathcal{O} (λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to mathcal{O} (λ2). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-Nc strong-coupling result. Our results suggest that the mathcal{O} (λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

Constraining the nonanalytic terms in the isospin-asymmetry expansion of the nuclear equation of state

We examine the properties of the isospin-asymmetry expansion of the nuclear equation of state from chiral two- and three-body forces. We focus on extracting the high-order symmetry energy coefficients that consist of both normal terms (occurring with even powers of the isospin asymmetry) as well as terms involving the logarithm of the isospin asymmetry that are formally nonanalytic around the expansion point of isospin-symmetric nuclear matter. These coefficients are extracted from numerically precise perturbation theory calculations of the equation of state coupled with a new set of finite difference formulas that achieve stability by explicitly removing the effects of higher-order terms in the expansion. We consider contributions to the symmetry energy coefficients from both two- and three-body interactions. It is found that the coefficients of the logarithmic terms are generically larger in magnitude than those of the normal terms from second-order perturbation theory diagrams, but overall the normal terms give larger contributions to the ground state energy. The high-order isospin-asymmetry terms are especially relevant at large densities where they affect the proton fraction in beta-equilibrium matter.

Higher-order regularity in local and nonlocal quantum gravity

In the present work we investigate the Newtonian limit of higher-derivative gravity theories with more than four derivatives in the action, including the non-analytic logarithmic terms resulting from one-loop quantum corrections. The first part of the paper deals with the occurrence of curvature singularities of the metric in the classical models. It is shown that in the case of local theories, even though the curvature scalars of the metric are regular, invariants involving derivatives of curvatures can still diverge. Indeed, we prove that if the action contains 2n+6 derivatives of the metric in both the scalar and the spin-2 sectors, then all the curvature-derivative invariants with at most 2n covariant derivatives of the curvatures are regular, while there exist scalars with 2n+2 derivatives that are singular. The regularity of all these invariants can be achieved in some classes of nonlocal gravity theories. In the second part of the paper, we show that the leading logarithmic quantum corrections do not change the regularity of the Newtonian limit. Finally, we also consider the infrared limit of these solutions and verify the universality of the leading quantum correction to the potential in all the theories investigated in the paper.

Importance of macroscopic polarization on vibrational properties and the robust nature of (001) surface states of SnTe

Here, we study the importance of macroscopic polarization for explaining the lattice dynamics of SnTe. Along with this, the robustness of (001) surface states is discussed for the practical application of this compound. The long range Coulomb forces using nonanalytical term correction are needed for proper explanation of experimental phonon modes with the Born effective charge's value of ∼5.5 (∼-5.5) for Sn (Te) atom. The peaks' positions of phonon density of states are in good agreement with the experimental observation. The Debye temperature for SnTe is found to be ∼189 K. We have also explored the possibility of protecting the (001) surface states via mirror and time-reversal symmetry. These surface states are expected to be robust against the point and line defects.

Constraints on the nuclear symmetry energy from asymmetric-matter calculations with chiral NN and 3N interactions

The nuclear symmetry energy is a key quantity in nuclear (astro)physics. It describes the isospin dependence of the nuclear equation of state (EOS), which is commonly assumed to be almost quadratic. In this work, we confront this standard quadratic expansion of the EOS with explicit asymmetric nuclear-matter calculations based on a set of commonly used Hamiltonians including two- and three-nucleon forces derived from chiral effective field theory. We study, in particular, the importance of non-quadratic contributions to the symmetry energy, including the non-analytic logarithmic term introduced by Kaiser [Phys.~Rev.~C \textbf{91}, 065201 (2015)]. Our results suggest that the quartic contribution to the symmetry energy can be robustly determined from the various Hamiltonians employed, and we obtain 1.00(8) MeV (or 0.55(8) MeV for the potential part) at saturation density, while the logarithmic contribution to the symmetry energy is relatively small and model-dependent. We finally employ the meta-model approach to study the impact of the higher-order contributions on the neutron-star crust-core transition density, and find a small 5\% correction.

Nonanalytic nonequilibrium field theory: Stochastic reheating of the Ising model

Many-body nonequilibrium steady states can be described by a Landau-Ginzburg theory if one allows nonanalytic terms in the potential. We substantiate this claim by working out the case of the Ising magnet in contact with a thermal bath and undergoing stochastic reheating: It is reset to a paramagnet at random times. By a combination of stochastic field theory and Monte Carlo simulations, we unveil how the usual φ4 potential is deformed by nonanalytic operators of intrinsic nonequilibrium nature. We demonstrate their infrared relevance at low temperatures by a renormalization-group analysis of the nonequilibrium steady state. The equilibrium ferromagnetic fixed point is thus destabilized by stochastic reheating and we identify the new nonequilibrium fixed point.1 MoreReceived 30 June 2020Accepted 28 November 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.043390Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsStatistical field theoryPhysical SystemsClassical spin modelsNonequilibrium lattice modelsNonequilibrium systemsTechniquesMean-field & cluster methodsMonte Carlo methodsRenormalization groupStatistical Physics

Chiral extrapolation of the magnetic polarizability of the neutral pion

The magnetic polarizability of the neutral pion has been calculated in the background magnetic-field formalism of Lattice QCD. In this investigation, the chiral extrapolation of these lattice results is considered in a formalism preserving the exact leading nonanalytic terms of chiral perturbation theory. The $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory and identify the leading contributions of quark-flow connected and disconnected diagrams. While electro-quenching does not impact the leading-loop contribution to the magnetic polarizability, the loops which generate the leading term have yet to be considered in lattice QCD simulations. Lattice QCD results are used to constrain the analytic terms in the chiral expansion and supplementing those with the two-loop result from chiral perturbation theory enables an evaluation of the polarizability at the physical quark mass. The resulting magnetic polarizability of the neutral pion is $\beta_{\pi^0}=3.44(19)^{\rm stat}(37)^{\rm syst}\times 10^{-4}$ fm$^3$, which lies just above the $1 \sigma$ error bound of the experimental measurement.

First principles calculation of mechanical, dynamical and thermodynamic properties of MnO2 with four crystal phases

MnO2 has four crystal phases, whose stability and vibrational properties can affect significantly its application. In this study, a spin-polarized DFT + U method was performed to investigate the structural, mechanical, lattice dynamical, and thermodynamic properties of α-, β-, γ- and δ-MnO2. The analysis of the mechanical properties and phonon dispersion curves confirmed that all four kinds of MnO2 were mechanically and dynamically stable. The calculated mechanical properties indicated that α- and β-MnO2 were ductile, while γ-MnO2 was brittle. The phonon dispersion curves and the phonon density of states were calculated using DFPT. The phonon vibrational frequencies were analyzed in detail by the LO-TO splitting considering the non-analytical term correction. Raman and infrared active normal modes were assigned and discussed briefly to resolve the uncertainty in experiment of the assignment for the four kinds of MnO2. The symmetry of Au, Au, B3u were IR characteristic band for α-, β-, γ-MnO2, and the symmetry of Ag, A1g, Ag, A1g were Raman characteristic band for α-, β-, γ- and δ-MnO2. Finally, the thermodynamic functions of the enthalpy change and the entropy were evaluated and compared with the experimental values.

Ultra-low lattice thermal conductivity and giant phonon–electric field coupling in hafnium dichalcogenide monolayers

Phonons in crystalline solids are of utmost importance in governing its lattice thermal conductivity (kL). In this work, kL in hafnium (Hf) dichalcogenide monolayers has been investigated based on ab initio DFT coupled to linearized Boltzmann transport equation together with single-mode relaxation-time approximation. Ultra-low kL found in HfS2 (2.19 W m−1 K−1), HfSe2 (1.23 W m−1 K−1) and HfSSe (1.78 W m−1 K−1) monolayers at 300 K, is comparable to that of the state-of-art bulk thermoelectric materials, such as, Bi2Te3 (1.6 W m−1 K−1), PbTe (2.2 W m−1 K−1) and SnSe (2.6 W m−1 K−1). Gigantic longitudinal-transverse optical (LO-TO) splitting of up to 147.7 cm−1 is noticed at the Brillouin zone-centre (Γ-point), which is much higher than that in MoS2 single layer (∼2 cm−1). It is driven by the colossal phonon–electric field coupling arising from the domination of ionic character in the interatomic bonds and Born effective or dynamical charges as high as 7.4e on the Hf ions, which is seven times that on Mo in MoS2 single layer. Enhancement in kL occurs in HfS2 (2.19 to 4.1 W m−1 K−1), HfSe2 (1.23 to 1.7 W m−1 K−1) and HfSSe (1.78 to 2.2 W m−1 K−1) upon the incorporation of the non-analytic correction term. Furthermore, the mode Grüneisen parameter is calculated to be as high as ∼2.0, at room temperature, indicating a strong anharmonicity. Moreover, the contribution of optical phonons to kL is found to be ∼12%, which is significantly high than that in single-layer MoS2. Large atomic mass of Hf (178.5 u), small phonon group velocities (4–5 km s−1), low Debye temperature (∼166 K), low bond and elastic stiffness (Young’s modulus ∼75 N m−1), small phonon lifetimes (∼6 ps), low specific heat capacity (∼17 J K−1 mol−1) and strong anharmonicity are collectively found to be the factors responsible for such a low kL. These findings would be immensely helpful in designing thermoelectric interconnects at the nanoscale and 2D material-based energy harvesters.

First-principles electronic structure, phonon properties, lattice thermal conductivity and prediction of figure of merit of FeVSb half-Heusler

In this work, we have studied the electronic structure of a promising thermoelectric half-Heusler FeVSb using FP-LAPW method and SCAN meta-GGA including spin–orbit coupling. Using the obtained electronic structure and transport calculations we try to address the experimental Seebeck coefficient S of FeVSb samples. The good agreement between the experimental and calculated S suggests the band gap could be ∼0.7 eV. This is supported by the obtained mBJ band gap of ∼0.7 eV. Further, we study and report the phonon dispersion, density of states and thermodynamic properties. The effect of long range Coulomb interactions on phonon frequencies are also included by nonanalytical term correction. Under quasi-harmonic approximation, the thermal expansion behaviour up to 1200 K is calculated. Using the first-principles anharmonic phonon calculations, the lattice thermal conductivity κ ph of FeVSb is obtained under single-mode relaxation time approximation considering the phonon-phonon interaction. At 300 K, the calculated κ ph is ∼18.6 W m−1 K−1 which is higher compared to experimental value. But, above 500 K the calculated κ ph is in good agreement with experiment. A prediction of figure of merit ZT and efficiency for p-type and n-type FeVSb is made by finding out optimal carrier concentration. At 1200 K, a maximum ZT of ∼0.66 and ∼0.44 is expected for p-type and n-type FeVSb, respectively. For p-type and n-type materials, maximum efficiency of ∼12.2% and ∼6.0% are estimated for hot and cold temperature of 1200 K and 300 K, respectively. A possibility of achieving n-type and p-type FeVSb by elemental doping/vacancy is also discussed. Our study is expected to help in further exploring the thermoelectric material FeVSb.

Exchange intervalley scattering and magnetic phase diagram of transition metal dichalcogenide monolayers

We analyze magnetic phases of monolayers of transition metal dichalcogenides that are two-valley materials with electron-electron interactions. The exchange intervalley scattering makes two-valley systems less stable to the spin fluctuations but more stable to the valley fluctuations. We predict a first-order ferromagnetic phase transition governed by the nonanalytic and negative cubic term in the free energy that results in a large spontaneous spin magnetization. Finite spin-orbit interaction leads to the out-of-plane Ising order of the ferromagnetic phase. Our theoretical prediction is consistent with the recent experiment on the electron-doped monolayers of ${\mathrm{MoS}}_{2}$ reported by Roch et al. [Nat. Nanotechnol. 14, 432 (2019)]. The proposed first-order phase transition can also be tested by measuring the linear magnetic field dependence of the spin susceptibility in the paramagnetic phase which is a direct consequence of the nonanalyticity of the free energy.

Crossover multiparameter equation of state: General procedure and demonstration with carbon dioxide

The multiparameter equation of state represents experimental data in wide ranges of temperature and density with superb accuracy. However, at the critical point, all classical models fail in describing the asymptotic behavior of thermodynamic properties, which is governed by the renormalization group (RG) theory. Using the crossover method, the classical models far from the critical point can be transformed to the RG theory at the critical point. Here we validate the procedure of combining the crossover method with the multiparameter equation of state through comparison with experimental data and the original multiparameter equation of state, and testing against the qualitative criterion of characteristic curves. We select carbon dioxide as a demonstration due to its data availability and qualification as a benchmark fluid for thermodynamic property modeling. We describe in detail the contribution of different types of terms in the crossover method and original multiparameter equation of state to thermodynamic properties. Furthermore, we propose twin Gaussian terms to compensate for the loss of accuracy near the coexistence curve upon removing the non-analytical terms and leave the analytical part of the formulation (terms and coefficients) unaltered. With a slight and acceptable loss of accuracy in the crossover region, the crossover method enforces the asymptotic singular behavior and critical exponents at the critical point. Far from the critical point, the present model transforms to the original model and retains the superb accuracy of the latter.

String theory integrands and supergravity divergences

At low energies, interactions of massless particles in type II strings compactified on a torus Td are described by an effective Wilsonian action mathcal{S} (Λ), consisting of the usual supergravity Lagrangian supplemented by an infinite series of higher-derivative vertices, including the much studied Δ4p + 6qℛ4 gravitational interactions. Using recent results on the asymptotics of the integrands governing four-graviton scattering at genus one and two, I determine the Λ-dependence of the coefficient of the above interaction, and show that the logarithmic terms appearing in the limit Λ → 0 are related to UV divergences in supergravity amplitudes, augmented by stringy interactions. This provides a strong consistency check on the expansion of the integrand near the boundaries of moduli space, in particular it elucidates the appearance of odd zeta values in these expansions. I briefly discuss how these logarithms are reflected in non-analytic terms in the low energy expansion of the string scattering amplitude.

Diverging Exchange Force and Form of the Exact Density Matrix Functional.

For translationally invariant one-band lattice models, we exploit the abinitio knowledge of the natural orbitals to simplify reduced density matrix functional theory (RDMFT). Striking underlying features are discovered. First, within each symmetry sector, the interaction functional F depends only on the natural occupation numbers n. The respective sets P_{N}^{1} and E_{N}^{1} of pure and ensemble N-representable one-matrices coincide. Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope E_{N}^{1}≡P_{N}^{1}, described by linear constraints D^{(j)}(n)≥0. For smaller systems, it follows as F[n]=[under ∑]i,i^{'}V[over ¯]_{i,i^{'}}sqrt[D^{(i)}(n)D^{(i^{'})}(n)]. This generalizes to systems of arbitrary size by replacing each D^{(i)} by a linear combination of {D^{(j)}(n)} and adding a nonanalytical term involving the interaction V[over ^]. Third, the gradient dF/dn is shown to diverge on the boundary ∂E_{N}^{1}, suggesting that the fermionic exchange symmetry manifests itself within RDMFT in the form of an "exchange force." All findings hold for systems with a nonfixed particle number as well and V[over ^] can be any p-particle interaction. As an illustration, we derive the exact functional for the Hubbard square.