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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Multireference Equation-of-Motion Driven Similarity Renormalization Group: Theoretical Foundations and Applications to Ionized States

We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for strongly correlated systems. The EOM step scales as O(N 5 ) with the basis set size N, allowing for efficient calculation of spectroscopic properties, such as transition energies and intensities. The IP-EOM-DSRG formalism is combined with three truncation schemes of the parent MR-DSRG theory: an iterative nonperturbative method with up to two-body excitations [MR-LDSRG(2)] and second- and third-order perturbative approximations [DSRG-MRPT2/3]. We benchmark these variants by computing (1) the vertical valence ionization potentials of a series of small molecules at both equilibrium and stretched geometries; (2) the spectroscopic constants of several low-lying electronic states of the OH, CN, N 2 + , and CO + radicals; and (3) the binding curves of low-lying electronic states of the CN radical. A comparison with experimental data and theoretical results shows that all three IP-EOM-DSRG methods accurately reproduce the vertical ionization potentials and spectroscopic constants of these systems. Notably, the DSRG-MRPT3 and MR-LDSRG(2) versions outperform several state-of-the-art multireference methods of comparable or higher cost.

Hamiltonians↗
DOE OSTI2026

One-Step Relativistic Driven Similarity Renormalization Group Multireference Perturbation Theory

We present an efficient implementation of a one-step relativistic second-order multireference perturbation theory based on the multireference driven similarity renormalization group (MR-DSRG) using the exact two-component (X2C) Hamiltonian, which we denote X2C-DSRG-MRPT2. We show that the X2C-DSRG-MRPT2 method can accurately capture spin–orbit coupling (SOC) effects in the electronic structure of strongly correlated systems containing elements across the periodic table. We further demonstrate that the X2C-DSRG-MRPT2 method, through its variational treatment of SOC effects, can yield spin–orbit splittings with mean absolute percentage errors consistently below 7% with respect to experimental values for systems containing up to sixth row elements. With its modest computational scaling (fourth power in system size for the perturbative step) and high accuracy, X2C-DSRG-MRPT2 provides a promising avenue for the routine treatment of relativistic effects in strongly correlated molecular systems.

Hamiltonians↗
DOE OSTI2021

Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) based on the ensemble normal ordering of Mukherjee and Kutzelnigg (1997). This ensemble averages over all microstates of a given total spin quantum number, and therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of 33 first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ molecules. A focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. The FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple- ζ basis set predicts the spin splittings of [Fe(H 2 O) 6 ] 2+ and [Fe(NH 3 ) 6 ] 2+ to be –35.7 and –17.1 kcal mol –1 , respectively, showing good agreement with the results of local CC theory with singles, doubles, and perturbative triples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Tensor renormalization group approach to the $O(2)$ models via symmetry-twisted partition functions

We investigate critical phenomena in the $O(2)$ models using symmetry-twisted partition functions that can be efficiently computed within the tensor renormalization group framework. We first demonstrate, taking the three-dimensional model as an example, that symmetry-twisted partition functions detect the spontaneous breaking of global continuous symmetry. We then consider the same model in two dimensions, where the Berezinskii--Kosterlitz--Thouless (BKT) transition occurs. Since symmetry-twisted partition functions directly provide the helicity modulus at a finite twist angle, we determine the BKT transition point. These results are presented based on Ref.~\cite{Akiyama:2026dzg}. Finally, in addition to the original paper~\cite{Akiyama:2026dzg}, we apply this approach to the two-dimensional generalized $O(2)$ model and confirm that it successfully identifies the phase transitions between the ferromagnetic and nematic phases, as well as between the nematic and paramagnetic phases.

Akiyama, Shinichiro [Tsukuba U., CCS; Tokyo U., IC↗
DOE OSTI2025

Quantum Chemical Density Matrix Renormalization Group Method Boosted by Machine Learning

The use of machine learning (ML) to refine low-level theoretical calculations to achieve higher accuracy is a promising and actively evolving approach known as Δ-ML. The density matrix renormalization group (DMRG) is a powerful variational approach widely used for studying strongly correlated quantum systems. High computational efficiency can be achieved without compromising accuracy. Here, we demonstrate the potential of a simple ML model to significantly enhance the performance of the quantum chemical DMRG method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Structure functions from renormalization group improved small x evolution

Abstract We perform the fit to the structure function $$F_2$$ F 2 data from HERA including terms due to the resummation at small x . The equation for the unintegrated gluon density is solved, previously established within the renormalization group improved small x framework. We find very good description of the structure function $$F_2$$ F 2 and its charm component $$F_2^c$$ F 2 c . The resulting unintegrated gluon density is found to be consistent with the calculations based on similar approaches available in the literature, with only slightly higher intercept value.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Renormalization group for nonminimal Φ 2 R couplings and gravitational contact interactions

Theories of scalars and gravity, with an Einstein-Hilbert term and nonminimal interactions, M 2 R / 2 - α Φ 2 R / 12 , have graviton exchange-induced contact interactions. These modify the renormalization group, leading to a discrepancy between the conventional calculations in the Jordan frame that ignore this effect (and are found to be incorrect), and the Einstein frame in which α does not exist. Thus, the calculation of quantum effects in the Jordan and Einstein frames does not generally commute with the transition from the Jordan to the Einstein frame. In the Einstein frame, though α is absent, for small steps in scale δ μ / μ infinitesimal contact terms ~ δ α are induced, that are then absorbed back into other couplings by the contact terms. This modifies the β -functions in the Einstein frame. In conclusion, we show how correct results can be obtained in a simple model by including this effect.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Renormalization group analysis of electromagnetic properties of the deuteron

The role of radiative corrections in low-energy nuclear physics is beginning to receive more scrutiny. We examine the impact of these corrections for the deuteron charge form factor and the radiative capture process np→dγ through the velocity renormalization group. In both cases, we find percent-level shifts in the relevant observables after evolving the subtraction velocity to the typical velocity of nucleons in the bound state. This suggests that electromagnetic corrections constitute a non-negligible source of uncertainty in existing few-body calculations.

Richardson, Thomas R↗
DOE OSTI2022

Systematics of E 2 strength in the s d shell with the valence-space in-medium similarity renormalization group

Recent developments in ab initio nuclear theory demonstrate promising results in medium- to heavy-mass nuclei. A particular challenge for many of the many-body methodologies, however, is an accurate treatment of the electric-quadrupole, E2, strength associated with collectivity. The valence-space in-medium similarity renormalization group (VS-IMSRG) is a particularly powerful method for accessing medium- and high-mass nuclei but has been found to underpredict E2 strengths. The purpose of this work is to evaluate the isospin dependence of this underprediction. We perform a systematic comparison of VS-IMSRG calculations with available literature. We make use of isoscalar and isovector contributions to the E2 matrix elements to assess isoscalar and isovector contributions to the missing strength. It is found that the E2 strength is consistent throughout T z =|12|, T z =|1|, T z =|32|, and T z =2 pairs within the sd shell. Furthermore, no isovector contribution to the deficiency is identified. A comparison with toy-models and coupled-cluster calculations is used to discuss potential origins of the missing strength, which arises from missing many-particle, many-hole excitations out of the model space. The absence of any significant isovector contribution to the missing E2 strength indicates that the E2 strength discrepancy, and therefore any correction, is largely independent of the isospin of the nuclei in question.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical 𝑂⁡(2) nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature 𝑇 𝑐 = 2.2017⁢(2) with the critical exponent 𝜈 = 0.663⁢(33) for the 3D 𝑂⁡(2) model. In addition, we also study the Berezinskii–Kosterlitz–Thouless (BKT) criticality of the 2D classical 𝑂⁡(2) model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, 𝑇 BKT = 0.8928⁢(2).

lattice field theory↗
DOE OSTI2024

Temporal entanglement entropy as a probe of renormalization group flow

The recently introduced concept of timelike entanglement entropy has sparked a lot of interest. Unlike the traditional spacelike entanglement entropy, timelike entanglement entropy involves tracing over a timelike subsystem. In this work, we propose an extension of timelike entanglement entropy to Euclidean space (“temporal entanglement entropy”), and relate it to the renormalization group (RG) flow. Specifically, we show that tracing over a period of Euclidean time corresponds to coarse-graining the system and can be connected to momentum space entanglement. We employ Holography, a framework naturally embedding RG flow, to illustrate our proposal. Within cutoff holography, we establish a direct link between the UV cutoff and the smallest resolvable time interval within the effective theory through the irrelevant $T\bar{T}$ deformation. Increasing the UV cutoff results in an enhanced capability to resolve finer time intervals, while reducing it has the opposite effect. Moreover, we show that tracing over a larger Euclidean time interval is formally equivalent to integrating out more UV degrees of freedom (or lowering the temperature). As an application, we point out that the temporal entanglement entropy can detect the critical Lifshitz exponent z in non-relativistic theories which is not accessible from spatial entanglement at zero temperature and density.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators

We present the second part of a systematic calculation of the two-loop anomalous dimensions for the low-energy effective field theory below the electroweak scale (LEFT): the baryon-number-violating sector at dimension six in the power counting. We obtain the results in two different schemes: in the algebraically consistent ’t Hooft-Veltman scheme for γ 5 , corrected for evanescent as well as chiral-symmetry-breaking effects through finite renormalizations; and in naive dimensional regularization, which in the considered sector of the theory does not lead to any ill-defined γ 5 -odd traces. Our results are of interest for a reanalysis of the constraints on physics beyond the Standard Model from proton-decay searches within an EFT framework at next-to-leading-logarithmic accuracy.

Baryon/Lepton Number Violation↗
DOE OSTI2026

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this paper, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Chemical calculations↗
DOE OSTI2022

Density matrix renormalization group description of the island of inversion isotopes F 28 – 33

Recent experiments have confirmed that the neutron-rich isotopes 28,29 F belong to the so-called island of inversion (IOI), a region of the nuclear chart around Z = 10 and N = 20 where nuclear structure deviates from the standard shell model predictions due to deformation and continuum effects. However, while the general principles leading to the IOI are relatively well understood, the details of the low-lying structure of the exotic fluorine isotopes 28–33 F are basically unknown. In this study, we perform large-scale shell model calculations including continuum states to investigate the properties of the neutron-rich isotopes 25–33 F, from a core of 24 O and using an effective two-body interaction with a small number of adjustable parameters in the central and tensor channels. We develop two models adjusted on experimentally confirmed states in 25,26 O and 25–27 F based on different assumptions concerning the positions of the neutron 0d 3/2 and 1p 3/2 shells, and solve the many-body problem using the density matrix renormalization group (DMRG) method for open quantum systems in an sd–fp model space. We obtain the first detailed spectroscopy of 25–33F in the continuum and show how the interplay between continuum effects and deformation explains the recent data on 28,29 F. Several deformed one- and two-neutron halo states are predicted in 29,31 F, and we provide some information about the possible structure of the heaviest fluorine isotopes. We also suggest several experimental studies of interest to constraint models and test the present predictions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗