Low-momentum Interactions Research Articles

Floquet nonadiabatic mixed quantum-classical dynamics in periodically driven solid systems.

In this paper, we introduce the Floquet mean-field dynamics and Floquet surface hopping approaches to study the nonadiabatic dynamics in periodically driven solid systems. We demonstrate that these two approaches can be formulated in both real and reciprocal spaces. Using the two approaches, we are able to simulate the interaction between electronic carriers and phonons under periodic drivings, such as strong light-matter interactions. Employing the Holstein and Peierls models, we show that strong light-matter interactions can effectively modulate the dynamics of electronic population and mobility. Notably, our study demonstrates the feasibility and effectiveness of modeling low-momentum carriers' interactions with phonons using a truncated reciprocal space basis, an approach impractical in real space frameworks. Moreover, we reveal that even with a significant truncation, carrier populations derived from surface hopping maintain greater accuracy compared to those obtained via mean-field dynamics. These results underscore the potential of our proposed methods in advancing the understanding of carrier-phonon interactions in various periodically driven materials.

Equation of state of superfluid neutron matter with low-momentum interactions

The behavior of the unbound neutrons in the inner crust of neutron stars is linked to various neutron-star characteristics such as glitches in the repetition rate of pulsars. This paper presents a novel calculation of low-density superfluid neutron matter using techniques and interactions previously applied to the study of finite nuclei. The starting point is a two-body interaction softened using renormalization-group techniques. The resulting interaction is used in a Hartree-Fock-Bogoliubov calculation that includes pairing. This provides a good starting point for the many-body perturbation expansion, and for including more sophisticated nuclear interactions in future work.

Description for N = 126 Isotones 210Po and 212Rn with Particle-Hole Excited Nucleon-Pair Approximation and Realistic Effective Interaction

In this paper, we study yrast states of two N=126 isotones 210Po and 212Rn using the nucleon-pair approximation with particle–hole excitations and using a low-momentum interaction Vlow–k renormalized from the free CD-Bonn NN potential. An overall good agreement with experimental level structures, B(E2)s, and B(E3)s, is achieved. We also calculate the probabilities of neutron particle–hole excitations in these yrast states, with a focus on negative-parity states, which reflect the roles played by the neutron negative-parity configurations of one-particle-one-hole excitations across the N=126 shell gap and the negative-parity configurations of valence proton particles involving the 0i13/2 orbit. The N=126 shell gap is discussed in terms of energies of neutron one-particle-one-hole excitations.

Low-momentum interactions for ultracold Fermi gases

We consider a two-component Fermi gas with a contact interaction from the BCS regime to the unitary limit. Starting from the idea that many-body effects should not depend on short-distance or high-momentum physics which is encoded in the s-wave scattering length, but only on momentum scales of the order of the Fermi momentum, we build effective low-momentum interactions that reproduce the scattering phase shifts of the contact interaction below some momentum cutoff. Inspired from recent successes of this method in nuclear structure theory, we use these interactions to describe the equation of state of the Fermi gas in the framework of Hartree-Fock-Bogliubov theory with perturbative corrections. In the BCS regime, there is a range of cutoffs where we obtain fully converged results. Near unitarity, convergence is not yet reached, but we obtain promising results for the ground-state energies close to the experimental ones. Limitations and possible extensions of the approach are discussed.

Nuclear response functions with low-momentum interactions

Linear density response functions for nuclear matter are calculated with separable 1S0 and 3S1 2-nucleon interactions obtained from experimental phase-shifts by inverse scattering techniques. It has been shown that results of nuclear matter binding energy Brueckner calculations with these potentials agree closely with those using realistic Bonn interactions. It has also been shown that low-momentum versions give binding energies (nearly) independent of momentum cut-offs $\Lambda \geq \sim 2$ fm-1. Shown here is that the $\Lambda = 2$ rank-one version of the separable interaction (for the S-states) yields a near agreement between a second-order and an all-order (Brueckner) binding energy calculation. Second order calculations of response functions are then made with this version using a method that Kwong and Bonitz used for the Coulomb gas. It is based on time-evolving two-time Green’s functions by Kadanoff-Baym (KB) equations. The effect of correlations, going beyond the conventional HF+RPA method, is included by “dressing” the Green’s function propagators with time-dependent complex self-energies in addition to the real HF-field. It would be of interest to see if the calculated response is also, like the binding energy, independent of cut-offs larger than $\sim 2$ fm-1. That would require using separable potentials of a higher rank, not accommodated by the present computer program. Some results with a 1.5 fm-1 cut-off are however also shown below together with those with a 2.0 fm-1 cut-off. The KB-equations are time-evolved until the nuclear medium is fully correlated. The time-dependent density response to an external perturbation is then registered and Fourier transformed to obtain energy-dependent density response functions. Most previous calculations have been made with in-medium effective (e.g., Gogny or Skyrme) interactions. The medium dependence is in the present calculations contained in the second-order terms.

Chiral Interactions up to Next-to-Next-to-Next-to-Leading Order and Nuclear Saturation.

We present an efficient MonteCarlo framework for perturbative calculations of infinite nuclear matter based on chiral two-, three-, and four-nucleon interactions. The method enables the incorporation of all many-body contributions in a straightforward and transparent way, and makes it possible to extract systematic uncertainty estimates by performing order-by-order calculations in the chiral expansion as well as the many-body expansion. The versatility of this new framework is demonstrated by applying it to chiral low-momentum interactions, exhibiting a very good many-body convergence up to fourth order. Following these benchmarks, we explore new chiral interactions up to next-to-next-to-next-to-leading order (N^{3}LO). Remarkably, simultaneous fits to the triton and to saturation properties can be achieved, while all three-nucleon low-energy couplings remain natural. The theoretical uncertainties of nuclear matter are significantly reduced when going from next-to-next-to-leading order to N^{3}LO.

Incorporating Brueckner-Hartree-Fock correlations in energy density functionals

Recently, a microscopically motivated nuclear energy density functional was derived by applying the density matrix expansion to the Hartree-Fock (HF) energy obtained from long-range chiral effective field theory two- and three-nucleon interactions. However, the HF approach cannot account for all many-body correlations. One class of correlations is included by Brueckner-Hartree-Fock (BHF) theory, which gives an improved definition of the one-body HF potential by replacing the interaction by a reaction matrix $G$. In this paper, we find that the difference between the $G$-matrix and the nucleon-nucleon potential $V_{\mathrm{NN}}$ can be well accounted for by a truncated series of contact terms. This is consistent with renormalization group decoupling generating a series of counterterms as short-distance physics is integrated out. The coefficients $C_{n}$ of the power series expansion $\sum C_{n}q^{n}$ for the counterterms are examined for two potentials at different renormalization group resolutions and at a range of densities. The success of this expansion for $G-V_{\mathrm{NN}}$ means we can apply the density matrix expansion at the HF level with low-momentum interactions and density-dependent zero-range interactions to model BHF correlations.

Screening and antiscreening of the pairing interaction in low-density neutron matter

We study pairing in low-density neutron matter including the screening interaction due to the exchange of particle-hole and RPA excitations. As bare force we employ the effective low-momentum interaction $V_{low\,k}$, while the Fermi-liquid parameters are taken from a phenomenological energy density functional (SLy4) which correctly reproduces the equation of state of neutron matter. At low density, we find screening, i.e., pairing is reduced, while at higher densities, we find anti-screening, i.e., pairing is enhanced. This enhancement is mostly due to the strongly attractive Landau parameter $f_0$. We discuss in detail the critical temperature $T_c$ in the limit of low densities and show that the suppression of $T_c$ predicted by Gor'kov and Melik-Barkhudarov can only be reproduced if the cutoff of the $V_{low\,k}$ interaction is scaled with the Fermi momentum. We also discuss the effect of non-condensed pairs on the density dependence of $T_c$ in the framework of the Nozi\`eres-Schmitt-Rink theory.

Global analysis of Skyrme forces with higher-order density dependencies**Supported by National Natural Science Foundation of China (11522538)

The density-dependent term in Skyrme forces is essential to simulate three-body and many-body correlations beyond the low-momentum two-body interaction. We speculate that a single density term may be insufficient and a higher-order density dependent term is added. The present work investigates the influence of higher-order density dependencies based on extended UNEDF0 and SkM* forces. Global descriptions of nuclear masses and charge radii are presented. The extended UNEDF0 force gives a global rms error on binding energies of 1.29 MeV. The influence on fission barriers and equation of state are also investigated. Perspectives to improve Skyrme forces are discussed, including global center-of-mass corrections and Lipkin-Nogami pairing corrections.

Nucleon-pair approximation with particle-hole excitations

In this paper, the formalism for the nucleon-pair approximation (NPA) with particle-hole excitations is developed. By using this approach, one is able to perform multiple-major-shell calculations. In this formulation, we use a particle-hole mixed representation, i.e., the particle-hole conjugate transformation is used for operators of the lower major shells, while operators of the upper major shells remain unchanged. We consider collective valence-particle pairs in the upper major shells, collective valence-hole pairs in the lower major shells, and collective pairs consisting of one valence particle in the upper shells and one valence hole in the lower shells to construct our model space. Matrix elements for the shell-model Hamiltonian, both for effective interactions and for phenomenological pairing plus multipole-multipole interactions, are derived in the nucleon-pair basis. As a special case, analytical formulas for doubly magic nuclei with excitations up to two-particle--two-hole are presented. To exemplify this approach, we calculate $^{100}\mathrm{Sn}$ considering both proton and neutron up to four-particle--four-hole excitations, where valence particles are in the 50-82 major shell and valence holes in the 28-50 major shell, with the low-momentum nucleon-nucleon interaction derived from the CD-Bonn potential.

Nucleon-deuteron scattering with the JISP16 potential

The nucleon-nucleon J-matrix Inverse Scattering Potential JISP16 is applied to elastic nucleon-deuteron (Nd) scattering and the deuteron breakup process at the lab. nucleon energies up to 135 MeV. The formalism of the Faddeev equations is used to obtain 3N scattering states. We compare predictions based on the JISP16 force with data and with results based on various NN interactions: the CD Bonn, the AV18, the chiral force with the semi-local regularization at the 5th order of the chiral expansion and with low-momentum interactions obtained from the CD Bonn force as well as with the predictions from the combination of the AV18 NN interaction and the Urbana IX 3N force. JISP16 provides a satisfactory description of some observables at low energies but strong deviations from data as well as from standard and chiral potential predictions with increasing energy. However, there are also polarization observables at low energies for which the JISP16 predictions differ from those based on the other forces by a factor of two. The reason for such a behavior can be traced back to the P-wave components of the JISP16 force. At higher energies the deviations can be enhanced by an interference with higher partial waves and by the properties of the JISP16 deuteron wave function. In addition, we compare the energy and angular dependence of predictions based on the JISP16 force with the results of the low-momentum forces obtained with different values of the momentum cutoff parameter. We found that such low-momentum forces can be employed to interpret the Nd elastic scattering data only below some specific energy which depends on the cutoff parameter. Since JISP16 is defined in a finite oscillator basis, it has properties similar to low momentum interactions and its application to the description of Nd scattering data is limited to a low momentum transfer region.

Four-body bound state calculations using three-dimensional low-momentum effective interaction Vlow-k

In this paper, we solve the coupled Yakubovsky integral equations for four-body (4B) bound state using the low-momentum effective two-body interaction [Formula: see text] in a three-dimensional (3D) approach, without using a partial wave (PW) decomposition. The renormalization group (RG) evolved interaction is constructed from spin-independent Malfliet–Tjon potential using the Lee–Suzuki method. The cutoff dependence of the 4B binding energy and wave function is investigated for a wide range of the momentum cutoff [Formula: see text] of [Formula: see text] interaction from 1.0 to 8.0[Formula: see text][Formula: see text].

Nuclear saturation in lowest-order Brueckner theory with two- and three-nucleon forces in view of chiral effective field theory

The nuclear saturation mechanism is discussed in terms of two-nucleon and three-nucleon interactions in chiral effective field theory (Ch-EFT), using the framework of lowest-order Brueckner theory. After the Coester band, which is observed in calculating saturation points with various nucleon-nucleon (NN) forces, is revisited using modern NN potentials and their low-momentum equivalent interactions, detailed account of the saturation curve of the Ch-EFT interaction is presented. The three-nucleon force (3NF) is treated by reducing it to an effective two-body interaction by folding the third nucleon degrees of freedom. Uncertainties due to the choice of the 3NF low-energy constants $c_D$ and $c_E$ are discussed. The reduction of the cutoff-energy dependence of the NN potential is explained by demonstrating the effect of the 3NF in the $^1$S$_0$ and $^3$S$_1$ states.

Shell-model study of quadrupole collectivity in light tin isotopes

A realistic shell-model study is performed for neutron-deficient tin isotopes up to mass $A=108$. All shell-model ingredients, namely, two-body matrix elements, single-particle energies, and effective charges for electric quadrupole transition operators, have been calculated by way of the many-body perturbation theory, starting from a low-momentum interaction derived from the high-precision CD-Bonn free nucleon-nucleon potential. The focus has been on the enhanced quadrupole collectivity of these nuclei, which is testified by the observed large $B(E2;{0}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})\mathrm{s}$. Our results give evidence of the crucial role played by the $Z=50$ cross-shell excitations that need to be taken into account explicitly to obtain a satisfactory theoretical description of light tin isotopes. We find also that a relevant contribution comes from the calculated neutron effective charges, whose magnitudes exceed the standard empirical values. An original double-step procedure has been introduced to reduce effectively the model space in order to overcome the computational problem.

Two-neutron transfer in Sn isotopes beyond theN=82shell closure

We have performed microscopic distorted-wave Born approximation calculations of differential cross sections for the two reactions $^{136}\mathrm{Sn}(p,t)^{134}\mathrm{Sn}$ and $^{134}\mathrm{Sn}(t,p)^{136}\mathrm{Sn}$, which are within reach of near-future experiments with radioactive ion beams. We have described the initial and final nuclear states in terms of the shell model, employing a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the available low-energy spectrum of $^{134}\mathrm{Sn}$. We discuss the main features of the predicted cross sections for the population of the low-lying yrast states in the two nuclei considered.

Binding Energy of ^(16)O in the Ring Diagram Method with Chiral Two- and Three-Nucleon Low Momentum Interactions

The recent developed low momentum nucleon-nucleon potential V_(low-k) obtained from integrating the high momentum part of a realistic potentials is adopted in the particle-particle hole-hole ring diagram calculation to study nuclear properties. The elementary NN interaction is chosen to be a chiral N^3LO two-nucleon potential V_(2N) with the inclusion of an in-medium three-nucleon (NNN) force V_(3N). The nuclear binding energy is accurately reproduced. Without this three-nucleon force, the nuclear binding energy is too weak, as is already known. The correction from the ring diagrams of order higher than 1 cannot be ignored. Comparison with old results using the Skyrme effective interactions is also made and discussed.

Triaxial deformation in nuclei with realisticNNinteractions

The structure of finite nuclei is investigated by employing an interaction model which is based on the low-momentum interaction $V_{lowk}$. It is supplemented by a density-dependent contact interaction fitted to reproduce the saturation properties of infinite nuclear matter within the Hartree-Fock approach. The calculations of finite nuclei are performed in a basis of plane waves discretized in a cartesian box of appropriate size. As a first example the structure of Ne isotopes is considered ranging from $^{18}$Ne to the neutron drip line. Rather good agreement is obtained for the bulk properties of these nuclei without any free parameter. The basis is also appropriate to describe other deformed nuclei and the transition from discrete nuclei to homogeneous matter which is supposed to occur in the crust of neutron stars.

Nuclear thermodynamics from chiral low-momentum interactions

We investigate the thermodynamic equation of state of isospin-symmetric nuclear matter with microscopic nuclear forces derived within the framework of chiral effective field theory. Two- and three-body nuclear interactions constructed at low resolution scales form the basis for a perturbative calculation of the finite-temperature equation of state. The nuclear force models and many-body methods are benchmarked against bulk properties of isospin-symmetric nuclear matter at zero temperature, which are found to be well reproduced when chiral nuclear interactions constructed at the lowest resolution scales are employed. The calculations are then extended to finite temperatures, where we focus on the liquid-gas phase transition and the associated critical point. The Maxwell construction is applied to construct the physical equation of state, and the value of the critical temperature is determined to be T_c =17.2-19.1 MeV, in good agreement with the value extracted from multifragmentation reactions of heavy ions.

Three-body bound state calculations using three-dimensional low-momentum interaction Vlow k

Three-dimensional Faddeev integral equations are solved for the three-body (3B) bound state problem without using the partial wave form of low-momentum two-body interaction |$V_{{\mathrm {low}}\,k}$| which is constructed from spin-independent Malfliet–Tjon V (MT-V) potential. The dependence of 3B binding energy on the cutoff momentum of |$V_{{\mathrm {low}}\,k}$| is investigated for a wide range of |$\Lambda $| from 1.0 to |$7.0\,{\mathrm {fm}}^{-1}$|⁠. The properties of the Faddeev components and 3B wave function are displayed and the effect of the number of grid points for momentum and angle variables on the accuracy and stability of the numerical results is studied by calculation of the expectation value of the total Hamiltonian.

Implicit Versus Explicit Renormalization of the NN Force: An S-Wave Toy Model

We use an S-wave toy model for the two-nucleon system to show that the implicit renormalization of a contact theory matches the explicit renormalization through a flow equation which integrates out the high momentum components. By fitting the low-momentum interaction with a new contact theory, we show that the running of the contact strengths in both original and fitted contact theories match over a wide cutoff range.