Effective Field Theory Methods Research Articles

Double honeycomb symmetry: Effective-field theory study

The double hexagonal lattice model is a new statistical model constructed by connecting two-dimensional hexagonal structured materials such as Graphene and Lie symmetries. The double hexagonal structure of this model appears in the G2 symmetry of Lie algebras. To investigate the magnetic properties of this new lattice model, an Ising-1/2 model was constructed with spin values σ = ±1. An effective-field theory (EFT) method was used with the differential operator technique to formulate the identity of the spin system, based on Callen's work. Different phase diagrams were established by varying the double-exchange interaction couplings and the super-exchange interaction coupling present in the model. The accurate results obtained by the EFT method were compared with those found by the mean-field approximation (MFA) method. The symmetry of the MFA diagrams was broken in the EFT diagrams. The critical temperature behavior was found to depend on the type of super-exchange ferromagnetism.

Investigating the magnetic and hysteretic properties of graphyne-based nanostructures: a comparative study of shape effects on critical temperatures, coercivity, and remanence

Our study aims to investigate the physical properties of graphyne-based nanostructures, with a particular focus on their magnetic and hysteretic features. We analyze the influence of shape on these properties in an Ising-type graphyne structure using the effective field theory (EFT) method. Our research focuses on the critical and compensation temperatures, coercivity, and remanence of the graphyne structure in different shapes, ranging from alpha (α) to beta (β) to gamma (γ). We use the magnetization curves and hysteresis loops obtained from central and intermediate spins. We also illustrate the behavior of the coercive field and remanent magnetization as well as hysteresis loop the effect of exchange interactions r and s as well as temperature. We observe N- and R- type compensation in the β graphyne, and L- and S- type compensations in the γ graphyne. We also find that the widest hysteresis is observed in γ graphyne.

Electronic, magnetic, half-Metallic, pressure-induced elastic and curie temperature predictions of Zr2RhTl Heusler alloy: DFT and EFT studies

ABSTRACT The DFT method investigated the total and partial magnetic moments, half-metallic characters, and pressure-dependent elastic properties of Zr2RhTl alloy. According to the ground state properties, the FM phase is more stable in energy than the AFM and NM phases. The Curie temperature value was obtained as 897.43 K with the help of the energy differences of the AFM and FM phases. The total magnetic moment of Zr2RhTl alloy was obtained as 2.00 µB/f.u. Partial magnetic moment values were obtained as 0.810, 0.506, 0.032, and 0.009 µB for Zr1, Zr2, Rh, and Tl atoms, respectively. All these total and partial magnetic moment values and Curie temperatures were supported by the Effective Field Theory (EFT) method. In addition, partial Curie temperatures of Zr2RhTl alloy were calculated by EFT separately for each element. The up-spins of Zr2RhTl alloy show metallic character in both the GGA and GGA + mBJ approximations, while the down-spins have band gaps of 0.698 and 0.699 eV, respectively. Electronic properties were also supported by GGA + U (U = 1, 2, 3 eV) interactions. Therefore, Zr2RhTl alloy is a true half-metallic ferromagnetic material. Zr2RhTl alloy was elastically stable, and the Debye temperature was calculated as 221.496 K at 0 GPa. All calculations obtained using two different methods (DFT and EFT) and two different approximations (GGA and GGA + mBJ) support each other. Therefore, Zr2RhTl alloy proved to be a very suitable material to be used as an alternative for spintronics.

Axion effective potentials induced by heavy sterile fermions

A model of (3 + 1)-dimensional leptogenesis, proposed previously by the authors, requires a CPT Violating (CPTV) background of the Kalb–Ramond (KR) axion field. The KR axion is a pseudoscalar, which is dual to the field strength of the spin-one field present in the massless gravitational multiplet in the theory of closed bosonic strings (compactified to four dimensions). Microscopic models for the emergence of such backgrounds are provided both by low-energy string-inspired gravitational theories with torsion (including (primordial) gravitational and axial gauge anomalies) and by Einstein–Cartan gravity, a closely related simpler model. In this work we examine the pseudoscalar quanta of the KR axion in this background using the methods of effective field theory. In our model for leptogenesis there is a single sterile right-handed neutrino (RHN) with mass m_N. At energies lower than m_N, an axion potential is derived by integrating out at one loop the sterile neutrino in the spirit of effective field theory. The stability of this axion potential is important for the viability of our model. The vacuum of this potential is generally metastable. The stability of the vacuum is determined by the ratio of the torsion-induced-axion coupling (which depends on the string mass scale) to m_N, which should be larger or equal to one, for the validity of our effective field theory. The vacuum is metastable only for axion couplings much larger than the sterile neutrino mass (large string mass scales, e.g. comparable to the four-dimensional Planck mass), with a lifetime much larger than the age of the observable Universe. By contrast, if axion couplings are comparable to the RHN mass the false vacuum is highly unstable, with a lifetime much smaller than the age of the observable Universe; in this case the CPTV leptogenesis scenario is not viable.

U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography

We study the quasi-hydrodynamics of a system with a softly broken U(1) global symmetry using effective field theory (EFT) and holographic methods. In the gravity side, we consider a holographic Proca model in the limit of small bulk mass, which is responsible for a controllable explicit breaking of the U(1) global symmetry in the boundary field theory. We perform a holographic Schwinger-Keldysh analysis, which allows us to derive the form of the boundary effective action in presence of dissipation. We compare our results with the previously proposed EFT and hydrodynamic theories, and we confirm their validity by computing the low-energy quasi-normal modes spectrum analytically and numerically. Additionally, we derive the broken holographic Ward identity for the U(1) current, and discuss the recently proposed novel transport coefficients for systems with explicitly broken symmetries. The setup considered is expected to serve as a toy model for more realistic situations where quasi-hydrodynamics is at work, such as axial charge relaxation in QCD, spin relaxation in relativistic systems, electric field relaxation in magneto-hydrodynamics, or momentum relaxation in condensed matter systems.

Minimal decoherence from inflation

We compute the rate with which super-Hubble cosmological fluctuations are decohered during inflation, by their gravitational interactions with unobserved shorter-wavelength scalar and tensor modes. We do so using Open Effective Field Theory methods, that remain under control at the late times of observational interest, contrary to perturbative calculations. Our result is minimal in the sense that it only incorporates the self-interactions predicted by General Relativity in single-clock models (additional interaction channels should only speed up decoherence). We find that decoherence is both suppressed by the first slow-roll parameter and by the energy density during inflation in Planckian units, but that it is enhanced by the volume comprised within the scale of interest, in Hubble units. This implies that, for the scales probed in the Cosmic Microwave Background, decoherence is effective as soon as inflation proceeds above ∼ 5 × 109 GeV. Alternatively, if inflation proceeds at GUT scale decoherence is incomplete only for the scales crossing out the Hubble radius in the last ∼ 13 e-folds of inflation. We also compute how short-wavelength scalar modes decohere primordial tensor perturbations, finding a faster rate unsuppressed by slow-roll parameters. Identifying the parametric dependence of decoherence, and the rate at which it proceeds, helps suggest ways to look for quantum effects.

Delta Baryon Spectroscopy in Lattice QCD

A variational analysis is performed within the framework of lattice QCD to extract the masses of the spin-3/2 positive parity Delta ^+ baryons, including radial excitations. 2 + 1 flavour dynamical gauge-field configurations provided by the PACS-CS collaboration via the ILDG are considered. To improve our interpolator basis, we perform an iterative process of source and sink smearing and solve a generalised eigenvalue problem using the resulting fermion operators. We obtain a clear signal for the ground and first excited states at a light quark mass corresponding to m_pi = 413 MeV. Furthermore, we show that one can use the eigenvectors obtained in this method to investigate the nature of these states, allowing us to classify our results as 1s and 2s states for the ground and first excited states respectively. Finally, we briefly highlight the method of Hamiltonian effective field theory which can be used to make comparison with quark model expectations.

Integrating out heavy scalars with modified equations of motion: Matching computation of dimension-eight SMEFT coefficients

The shift in focus towards searches for physics beyond the Standard Model (SM) employing model-independent Effective Field Theory (EFT) methods necessitates a rigorous approach to matching to guarantee the validity of the obtained results and constraints. The limits on the leading dimension-six EFT effects can be rather inaccurate for LHC searches that suffer from large uncertainties while exploring an extensive energy range. Similarly, precise measurements can, in principle, test the subleading effects of the operator expansion. In this work, we present an algorithmic approach to automatise matching computations for dimension-eight operators for generic scalar extensions with proper implementation of equations of motion. We devise a step-by-step procedure to obtain the dimension-eight Wilson coefficients (WCs) in a non-redundant basis to arrive at complete matching results. We apply this formalism to a range of scalar extensions of the SM and provide tree-level and loop-suppressed results. Finally, we discuss the relevance of the dimension-eight operators for a range of phenomenological analyses, particularly focusing on Higgs and electroweak physics.

Effective master equations for two accelerated qubits

We revisit the problem involving two constantly accelerating Unruh-DeWitt detectors using Open Effective Field Theory methods. We study the time evolution of the joint detector state using a Markovian approximation which differs from the standard one taken in the literature. We show that this Markovian limit already implies the complete positivity of the dynamical evolution map without invoking the rotating wave approximation (RWA), in contrast to standard derivations of open system master equations. By calculating explicitly the domain of validity of this Markovian approximation, we argue that the lack of complete positivity in the usual microscopic derivation stems from the (subtle) fact that the Redfield equation is used outside its domain of validity. We give two well-known cases studied in the literature that violate the validity of the Markovian approximation: (i) the ``stacked trajectory'' limit (when detector trajectories are taken to be on top of one another), and (ii) large gap-to-acceleration ratio. Since Markovian dynamics with or without RWA can lead to different qualitative predictions for entanglement dynamics, our work emphasizes the need to properly track the regime of validity of all approximations.

Continuous transition between Ising magnetic order and a chiral spin liquid

The competition between fractionalized spin-liquid states and magnetically ordered phases is an important paradigm in frustrated magnetism. Spin-orbit coupled Mott insulators with Ising-like magnetic anisotropies, such as Kitaev materials, are a particularly rich playground to explore this competition. In this work, we use effective field theory methods to show that a direct quantum phase transition can occur in two-dimensional (2D) Ising spin systems between a topologically ordered chiral spin liquid and a phase with magnetic long-range order. Such a transition can be protected by lattice symmetries and is described by a theory of massless Majorana fields coupled to non-Abelian $SO(N)$ gauge fields with a Chern-Simons term. We further show that Euclidean Majorana zero modes bound to $\mathbb{Z}_2$ monopole-instantons in the emergent non-Abelian gauge field are key to understanding spontaneous symmetry breaking in the ordered phase.

Effective Field Theory Description of Horizon-Fluid Determines the Scrambling Time

Black hole horizons interact with external fields when matter or energy falls through them. Such non-stationary black hole horizons can be described using viscous fluid equations. This work attempts to describe this process using effective field theory methods. Such a description can provide important insights beyond classical black hole physics. In this work, we construct a low-energy effective field theory description for the horizon-fluid of a 4-dimensional, asymptotically flat, Einstein black hole. The effective field theory of the dynamical horizon has two ingredients: degrees of freedom involved in the interaction with external fields and symmetry. The dual requirements of incorporating near-horizon symmetries (S1 diffeomorphism) and possessing length scales due to external perturbations are naturally satisfied if the theory on the non-stationary black hole horizon is a deformed Conformal Field Theory (CFT). For the homogeneous external perturbations, at the lowest order, this leads to a (2+1)-dimensional massive scalar field where the mass is related to the extent of the deformation of the CFT. We determine the mass by obtaining the correlation function corresponding to the effective field and relating it to the bulk viscosity of the horizon-fluid. Additionally, we show that the coefficient of bulk viscosity of the horizon-fluid determines the time required for black holes to scramble. Furthermore, we argue that matter-field modes with energy less than meff falling into the horizon thermalize more slowly. Finally, we construct a microscopic toy model for the horizon-fluid that reduces to the effective field theory with a single scalar degree of freedom. We then discuss the usefulness of the effective field model in understanding how information escapes from a black hole at late times.

Four-vector optical Dirac equation and spin-orbit interaction of structured light

The spin-orbit interaction of light is a crucial concept for understanding the electromagnetic properties of a material and realizing the spin-controlled manipulation of optical fields. Achieving these goals requires a complete description of spin-dependent optical phenomena in the context of vector-wave mechanics. We develop an extended Dirac theory for optical fields in generic media, which was found to be akin to a non-Hermitian chiral extension of massive fermions with anomalous magnetic momenta moving in an external pseudomagnetic field. This similarity allows us to investigate the optical behaviors of a material by effective field-theory methods and can find wide applications in metamaterials, photonic topological insulators, etc. We demonstrate this method by studying the spin-orbit interaction of structured light in a spin-degenerate medium and inhomogeneous isotropic medium, which leads to both spin-orbital Hall effects and spin-to-orbital angular momentum conversion. Of importance, our approach provides simple and clear physical insight into the spin-orbit interaction of light in generic media, and could potentially bridge our understanding of topological insulators between electronic and photonic systems.

Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays

Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a new strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model, albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless Z2 spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state 'Kitaev materials' and, more generally, spotlights a new angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.

Analyzing rotational bands in odd-mass nuclei using effective field theory and Bayesian methods

We recently developed an Effective Field Theory (EFT) for rotational bands in odd-mass nuclei. Here we use EFT expressions to perform a Bayesian analysis of data on the rotational energy levels of 99Tc, 155,157Gd, 159Dy, 167,169Er, 167,169Tm, 183W, 235U and 239Pu. The error model in our Bayesian analysis includes both experimental and EFT truncation uncertainties. It also accounts for the fact that low-energy constants (LECs) at even and odd orders are expected to have different sizes. We use Markov Chain Monte Carlo (MCMC) sampling to explore the joint posterior of the EFT and error-model parameters and show both the LECs and the breakdown scale can be reliably determined. We extract the LECs up to fourth order in the EFT and find that, provided we correctly account for EFT truncation errors in our likelihood, results for lower-order LECs are stable as we go to higher orders. LEC results are also stable with respect to the addition of higher-energy data. We extract the expansion parameter for all the nuclei listed above and find a clear correlation between the extracted and the expected value of the inverse breakdown scale, W, based on the single-particle and vibrational energy scales. However, the W that actually determines the convergence of the EFT expansion is markedly smaller than would be naively expected based on those scales.

The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach

Within an effective field theory method to general relativity, we calculate the fifth-order post–Newtonian (5PN) Hamiltonian dynamics also for the tail terms, extending earlier work on the potential contributions, working in harmonic coordinates. Here we calculate independently all (local) 5PN far-zone contributions using the in–in formalism, on which we give a detailed account. The five expansion terms of the Hamiltonian in the effective one body (EOB) approach, q82,q63,q44,d5¯ and an, can all be determined from the local contributions to the periastron advance Kloc,h(Eˆ,j), without further assumptions on the structure of the symmetric mass ratio, ν, of the expansion coefficients of the scattering angle χk. The O(ν2) contributions to the 5PN EOB parameters have been unknown in part before. We perform comparisons of our analytic results with the literature and also present numerical results on some observables.

Λ and the Limits of Effective Field Theory

AbstractThe cosmological constant problem stems from treating quantum field theory and general relativity as an effective field theory (EFT). We argue that the problem is a reduction ad absurdum and that one should reject the assumption that general relativity can generically be treated as an EFT. This marks a failure of naturalness and provides an internal signal that EFT methods do not apply in all spacetime domains. We then take an external view, showing that the assumptions for using EFTs are violated in general relativistic domains where Λ is relevant. We highlight some ways forward that do not depend on naturalness.

N=4 supersymmetric Yang-Mills thermodynamics from effective field theory

The free energy density of $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions is derived through second order in the 't Hooft coupling $\ensuremath{\lambda}$ at finite temperature using effective-field theory methods. The contributions to the free energy density at this order come from the hard scale $T$ and the soft scale $\sqrt{\ensuremath{\lambda}}T$. The effects of the scale $T$ are encoded in the coefficients of an effective three-dimensional field theory that is obtained by dimensional reduction at finite temperature. The effects of the electric scale $\sqrt{\ensuremath{\lambda}}T$ are taken into account by perturbative calculations in the effective theory.

Cosmological trans-Planckian conjectures are not effective

It is remarkable that the primordial fluctuations as revealed by the CMB coincide with what quantum fluctuations would look like if they were stretched across the sky by accelerated cosmic expansion. It has been observed that this same stretching also brings very small — even trans-Planckian — length scales up to observable sizes if extrapolated far enough into the past. This potentially jeopardizes later descriptions of late-time cosmology by introducing uncontrolled trans-Planckian theoretical errors into all calculations. Recent speculations, such as the Trans-Planckian Censorship Conjecture (TCC), have been developed to avoid this problem. We revisit old arguments why the consistency of (and control over) the Effective Field Theory (EFT) governing late-time cosmology is not necessarily threatened by the descent of modes due to universal expansion, even if EFT methods may break down at much earlier times. Failure of EFT methods only poses a problem if late-time predictions rely on non-adiabatic behaviour at these early times (such as is often true for bouncing cosmologies, for example). We illustrate our arguments using simple non-gravitational examples such as slowly rolling scalar fields and the spacing between Landau levels for charged particles in slowly varying magnetic fields, for which similar issues arise and are easier to understand. We comment on issues associated with UV completions. Our arguments need not invalidate speculative ideas like the TCC but suggest they are not required by the present evidence.

Beyond the Standard Model effective field theory: The singlet extended Standard Model

One of the assumptions of simplified models is that there are a few new particles and interactions accessible at the LHC and all other new particles are heavy and decoupled. The effective field theory (EFT) method provides a consistent method to test this assumption. Simplified models can be augmented with higher order operators involving the new particles accessible at the LHC. Any UV completion of the simplified model will be able to match onto these beyond the Standard Model EFTs (BSM-EFT). In this paper we study the simplest simplified model: the Standard Model extended by a real gauge singlet scalar. In addition to the usual renormalizable interactions, we include dimension-5 interactions of the singlet scalar with Standard Model particles. As we will show, even when the cutoff scale is 3 TeV, these new effective interactions can drastically change the interpretation of Higgs precision measurements and scalar searches. In addition, we discuss how power counting in a BSM-EFT depends strongly on the processes and parameter space under consideration. Finally, we propose a $\chi^2$ method to consistently combine the limits from new particle searches with measurements of the Standard Model. Unlike imposing a hard cut off on heavy resonance rates, our method allows fluctuations in individual channels that are consistent with global fits.

Effects of short-distance modifications to general relativity in spinning binary systems

We investigate the possibility of testing short distance modifications to General Relativity via higher curvature terms in the fundamental gravity Lagrangian by analysing their impact on observations of spinning astronomical binary systems. By using effective field theory methods applied to the 2-body problem, generic lower bounds on the short-distance scale accompanying high curvature terms can be set. In particular we extend known results by deriving spin-dependent effects in binding energy, radiation emission process, and spin precession equations in binary systems, which are the fundamental ingredients to observe spin-dependent effects in gravitational wave detections from compact binary coalescences and spin precession in double binary pulsars.