Interacting Field Theory Research Articles

Entanglement renormalization for interacting field theories

A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through a class of variational non-Gaussian wavefunctionals for which expectation values of local operators can be efficiently calculated analytically and in a closed form. The method consists of a series of scale-dependent nonlinear canonical transformations on the fields of the theory under consideration. Here, the $\lambda\, \phi^4$ and the sine-Gordon scalar theories are used to illustrate how non-perturbative effects far beyond the Gaussian approximation are obtained by considering the energy functional and the correlation functions of the theory.

Essential elements for nuclear binding

How does nuclear binding emerge from first principles? Our current best understanding of nuclear forces is based on a systematic low-energy expansion called chiral effective field theory. However, recent ab initio calculations of nuclear structure have found that not all chiral effective field theory interactions give accurate predictions with increasing nuclear density. In this letter we address the reason for this problem and the first steps toward a solution. Using nuclear lattice simulations, we deduce the minimal nuclear interaction that can reproduce the ground state properties of light nuclei, medium-mass nuclei, and neutron matter simultaneously with no more than a few percent error in the energies and charge radii. We find that only four parameters are needed. With these four parameters one can accurately describe neutron matter up to saturation density and the ground state properties of nuclei up to calcium. Given the absence of sign oscillations in these lattice Monte Carlo simulations and the mild scaling of computational effort scaling with nucleon number, this work provides a pathway to high-quality simulations in the future with as many as one or two hundred nucleons.

Neutron stars within the Skyrme model

The Skyrme model is a low energy effective field theory of strong interactions where nuclei and baryons appear as collective excitations of pionic degrees of freedom. In the last years, there has been a revival of Skyrme’s ideas and new related models, and some of them with BPS bounds (topological lower energy bounds) have been proposed. It is the aim of this paper to review how they can be applied to the study of neutron stars allowing for a description by means of topological solitons. We will focus on different aspects as the equation of state or the mass-radius relation, where we find that high maximal masses are supported.

Microscopically based energy density functionals for nuclei using the density matrix expansion

While ab initio many-body techniques have been able to successfully describe the properties of light and intermediate mass nuclei based on chiral effective field theory interactions, neutron-rich nuclei still remain out of reach for these methods. Conversely, energy density functional approaches can be used to calculate properties of heavy nuclei but rely mostly on phenomenological interactions. A usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces was presented recently. The first component of this new set of functionals corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. The exchange term, which is a functional of the non-local density, is transformed into a local functional by applying the density matrix expansion. In order to reduce the computational cost due to the direct implementation of non-separable, local interactions in the Hartree term, we use an approximation to represent the regularized Yukawa functions in terms of a sum of (separable) Gaussian functions. These proceedings analyze the accuracy of such an approximation in terms of the number of Gaussian functions and look for an optimal value that gives an acceptable level of accuracy while maintaining the computational memory requirements in a many-body calculation as low as possible.

78Ni revealed as a doubly magic stronghold against nuclear deformation.

Nuclear magic numbers correspond to fully occupied energy shells of protons or neutrons inside atomic nuclei. Doubly magic nuclei, with magic numbers for both protons and neutrons, are spherical and extremely rare across the nuclear landscape. Although the sequence of magic numbers is well established for stable nuclei, experimental evidence has revealed modifications for nuclei with a large asymmetry between proton and neutron numbers. Here we provide a spectroscopic study of the doubly magic nucleus 78Ni, which containsfourteen neutrons more thanthe heavieststable nickel isotope. We provide direct evidence of its doubly magic nature, which is also predicted by ab initio calculations based on chiral effective-field theory interactions and the quasi-particle random-phase approximation. Our results also indicate the breakdown of the neutron magic number 50 and proton magic number 28 beyond this stronghold, caused by a competing deformed structure. State-of-the-art phenomenological shell-model calculations reproduce this shape coexistence, predicting a rapid transition from spherical to deformed ground states, with 78Ni as the turning point.

Ab initio description of collectivity for sd shell nuclei

In the present work, we have reported shell model results for open shell nuclei Ne, Mg and Si isotopes with $10 \leq N \leq 20$ in $sd$-shell model space. We have performed calculations in $sd$ shell with two $ab~initio$ approaches: in-medium similarity renormalization group (IM-SRG) and coupled-cluster (CC) theory. We have also performed calculations with phenomenological USDB interaction and chiral effective field theory based CEFT interaction. The results for rotational spectra and $B(E2;2_1^+\rightarrow 0_1^+)$ transitions are reported for even-mass isotopes. The IM-SRG and CC results are in reasonable agreement with the experimental data except at $N$ =20. This demonstrates a validity of $ab~initio$ description of deformation for doubly open-shell nuclei for $sd$ shell. To see the importance of $pf$ orbitals, we have also compared our results with SDPF-MU interaction by taking account of $2p-2h$ and $4p-4h$ configurations in $sd$-$pf$-shell model space.

Stable interactions in higher derivative field theories of derived type

We consider the general higher derivative field theories of derived type. At free level, the wave operator of derived-type theory is a polynomial of the order $n\geq 2$ of another operator $W$ which is of the lower order. Every symmetry of $W$ gives rise to the series of independent higher order symmetries of the field equations of derived system. In its turn, these symmetries give rise to the series of independent conserved quantities. In particular, the translation invariance of operator $W$ results in the series of conserved tensors of the derived theory. The series involves $n$ independent conserved tensors including canonical energy-momentum. Even if the canonical energy is unbounded, the other conserved tensors in the series can be bounded, that will make the dynamics stable. The general procedure is worked out to switch on the interactions such that the stability persists beyond the free level. The stable interaction vertices are inevitably non-Lagrangian. The stable theory, however, can admit consistent quantization. The general construction is exemplified by the order $N$ extension of Chern-Simons coupled to the Pais-Uhlenbeck-type higher derivative complex scalar field.

Flavor violating Higgs couplings in minimal flavor violation

Motivated by the recent LHC data on the lepton-flavor violating (LFV) decays h → ℓ1ℓ2 and Bs,d → ℓ1ℓ2, we study the Higgs-mediated flavor-changing neutral current (FCNC) interactions in the effective field theory (EFT) approach without and with the minimal flavor violation (MFV) hypothesis, and concentrate on the later. After considering the B and K physics data, the various LFV processes, and the LHC Higgs data, severe constraints on the Higgs FCNC couplings are derived, which are dominated by the LHC Higgs data, the {B}_s-{overline{B}}_s mixing, and the μ → eγ decay. In the general case and the MFV framework, allowed ranges of various observables are obtained, such as mathrm{mathcal{B}} (Bs → ℓ1ℓ2), mathrm{mathcal{B}} (h → ℓ1ℓ2), mathrm{mathcal{B}} (h → q1q2), and the branching ratio of μ → e conversion in Al. Future prospects of searching for the Higgs FCNC interactions at the low-energy experiments and the LHC are discussed.

Long-range interactions of kinks

We present a computational analysis of the long-range interactions of solitary waves in higher-order field theories. Our vehicle of choice is the $\varphi^8$ field theory, although we explore similar issues in example $\varphi^{10}$ and $\varphi^{12}$ models. In particular, we discuss the fundamental differences between the latter higher-order models and the standard $\varphi^4$ model. Upon establishing the power-law asymptotics of the model's solutions' approach towards one of the steady states, we make the case that such asymptotics require particular care in setting up multi-soliton initial conditions. A naive implementation of additive or multiplicative ans\"atze gives rise to highly pronounced radiation effects and eventually leads to the illusion of a repulsive interaction between a kink and an antikink in such higher-order field theories. We propose and compare several methods for how to "distill" the initial data into suitable ans\"atze, and we show how these approaches capture the attractive nature of interactions between the topological solitons in the presence of power-law tails (long-range interactions). This development paves the way for a systematic examination of solitary wave interactions in higher-order field theories and raises some intriguing questions regarding potential experimental observations of such interactions. As an Appendix, we present an analysis of kink-antikink interactions in the example models via the method of collective coordinates.

How (not) to renormalize integral equations with singular potentials in effective field theory

We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an "underlying fundamental theory" and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.

Generalised Born-Infeld models, Lax operators and the mathrm{T}overline{mathrm{T}} perturbation

Surprising links between the deformation of 2D quantum field theories induced by the composite mathrm{T}overline{mathrm{T}} operator, effective string models and the AdS/CFT correspondence, have recently emerged. The purpose of this article is to discuss various classical aspects related to the deformation of 2D interacting field theories. Special attention is given to the sin(h)-Gordon model, for which we were able to construct the mathrm{T}overline{mathrm{T}} -deformed Lax pair. We consider the Lax pair formulation to be the first essential step toward a more satisfactory geometrical interpretation of this deformation within the integrable model framework.Furthermore, it is shown that the 4D Maxwell-Born-Infeld theory, possibly with the addition of a mass term or a derivative-independent potential, corresponds to a natural extension of the 2D examples. Finally, we briefly comment on 2D Yang-Mills theory and propose a modification of the heat kernel, for a generic surface with genus p and n boundaries, which fully accounts for the mathrm{T}overline{mathrm{T}} contribution.

Higher-Spin Gauge Theories and Bulk Locality.

We present a no-go result on consistent Noether interactions among higher-spin gauge fields on anti-de Sitter space-times. We show that there is a nonlocal obstruction at the classical level to consistent interacting field theory descriptions of massless higher-spin particles that are described in the free limit by the free Fronsdal action, under the assumption that such theories arise from the gauging of a global higher-spin symmetry. Our result suggests that the Fronsdal program for introducing interactions among higher-spin gauge fields cannot be completed without introducing new guiding principles, which could potentially lie beyond the framework of classical field theory.

Neutron-proton scattering with lattice chiral effective field theory at next-to-next-to-next-to-leading order

We present a new lattice formulation of chiral effective field theory interactions with a simpler decomposition into spin channels. With these interactions the process of fitting to the empirical scattering phase shifts is simplified, and the resulting lattice phase shifts are more accurate than in previous studies. We present results for the neutron-proton system up to next-to-next-to-next-to-leading order for lattice spacings of $1.97$, $1.64$, $1.32$, and $0.99~{\rm fm}$. Our results provide a pathway to $\textit{ab initio}$ lattice calculations of nuclear structure, reactions, and thermodynamics with accurate and systematic control over the chiral nucleon-nucleon force.

Charge and magnetic properties of three-nucleon systems in pionless effective field theory

A method to calculate the form factor for an external current with non-derivative coupling for the three-body system in an effective field theory (EFT) of short-range interactions is shown. Using this method the point charge radius of ${}^3\mathrm{He}$ is calculated to next-to-next-to-leading order (NNLO) in pionless EFT ($\mathrm{EFT}(\not{\!\pi})$), and the magnetic moment and magnetic radius of ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ are calculated to next-to-leading order (NLO). For the ${}^3\mathrm{He}$ charge and magnetic form factors Coulomb interactions are ignored. The ${}^3\mathrm{He}$ point charge radius is given by 1.74(4) fm at NNLO. This agrees well with the experimental ${}^3\mathrm{He}$ point charge radius of 1.7753(54) fm [Angeli and Marinova, At. Data Nucl. Data Tables 99, 69 (2013)]. The ${}^3\mathrm{H}$ (${}^3\mathrm{He}$) magnetic moment in units of nuclear magnetons is found to be 2.92(35) (-2.08(25)) at NLO in agreement with the experimental value of 2.979 (-2.127). For ${}^3\mathrm{H}$ (${}^3\mathrm{He}$) the NLO magnetic radius is 1.78(11) fm (1.85(11) fm) which agrees with the experimental value of 1.840(182) fm (1.965(154) fm) [I. Sick, Prog. Part. Nucl. Phys. 47, 245 (2001)]. The fitting of the low-energy constant $L_{1}$ of the isovector two-body magnetic current and the consequences of Wigner-SU(4) symmetry for the three-nucleon magnetic moments are also discussed.

Large-cutoff behavior of local chiral effective field theory interactions

Interactions from chiral effective field theory have been successfully employed in a broad range of \textit{ab initio} calculations of nuclei and nuclear matter, but it has been observed that most results of few- and many-body calculations experience a substantial residual regulator and cutoff dependence. In this work, we investigate the behavior of local chiral potentials at leading order under variation of the cutoff scale for different local regulators. When varying the cutoff, we require that the resulting interaction produces no spurious bound states in the deuteron channel. We find that, for a particular choice of leading-order operators, nucleon-nucleon phase shifts and the deuteron ground-state energy converge to cutoff-independent plateaus, for all regulator functions we investigate. This observation may enable improved calculations with chiral Hamiltonians that also include three-nucleon interactions.

Constraining the Speed of Sound inside Neutron Stars with Chiral Effective Field Theory Interactions and Observations

Abstract The dense matter equation of state (EOS) determines neutron star (NS) structure but can be calculated reliably only up to one to two times the nuclear saturation density, using accurate many-body methods that employ nuclear interactions from chiral effective field theory constrained by scattering data. In this work, we use physically motivated ansatzes for the speed of sound c S at high density to extend microscopic calculations of neutron-rich matter to the highest densities encountered in stable NS cores. We show how existing and expected astrophysical constraints on NS masses and radii from X-ray observations can constrain the speed of sound in the NS core. We confirm earlier expectations that c S is likely to violate the conformal limit of , possibly reaching values closer to the speed of light c at a few times the nuclear saturation density, independent of the nuclear Hamiltonian. If QCD obeys the conformal limit, we conclude that the rapid increase of c S required to accommodate a 2 M ⊙ NS suggests a form of strongly interacting matter where a description in terms of nucleons will be unwieldy, even between one and two times the nuclear saturation density. For typical NSs with masses in the range of 1.2–1.4 M ⊙, we find radii between 10 and 14 km, and the smallest possible radius of a 1.4 M ⊙ NS consistent with constraints from nuclear physics and observations is 8.4 km. We also discuss how future observations could constrain the EOS and guide theoretical developments in nuclear physics.

From Few to Many Body Degrees of Freedom

Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the many-body problem by substituting the full, microscopic interactions by pseudopotentials which are designed to reproduce collisional information at specified energies, or binding energies in the few-body sector. These simplified interactions yield more tractable theories of the many-body problem, and are equivalent to effective field theory of interactions. Direct methods, which so far are most useful in one spatial dimension, have the goal of attacking the many-body problem at once by using few-body information only. Here, I will present non-perturbative direct methods to study one-dimensional fermionic and bosonic gases in one dimension.

Double-folding potentials from chiral effective field theory

The determination of nucleus–nucleus potentials is important not only to describe the properties of the colliding system, but also to extract nuclear-structure information and for modelling nuclear reactions for astrophysics. We present the first determination of double-folding potentials based on chiral effective field theory at leading, next-to-leading, and next-to-next-to-leading order. To this end, we construct new soft local chiral effective field theory interactions. We benchmark this approach in the 16O–16O system, and present results for cross sections computed for elastic scattering up to 700 MeV in energy, as well as for the astrophysical S-factor of the fusion reaction.

Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective field theory interactions. In this work, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei with $3\le A\le16$. Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. The outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to $^{16}$O, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei.

Effective-range corrections to the ground-state energy of the weakly-interacting Bose gas in two dimensions

Nonuniversal effects due to leading effective-range corrections are computed for the ground-state energy of the weakly-coupled repulsive Bose gas in two spatial dimensions. Using an effective field theory of contact interactions, these corrections are computed first by considering fluctuations around the mean-field free energy of a system of interacting bosons. This result is then confirmed by an exact calculation in which the energy of a finite number of bosons interacting in a square with period boundary conditions is computed and the thermodynamic limit is explicitly taken.