Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Renormalization Group”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
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 OSTI2014

Low-lying excited states in armchair polyacene within Pariser-Parr-Pople model: A density matrix renormalization group study

We studied the nature of the ground state and low-lying excited states of armchair polyacene oligomers (Polyphenanthrene) within long-range Pariser-Parr-Pople model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. The ground state of all armchair polyacenes studied is found to be singlet. The results show that lowest singlet dipole allowed excited state has higher energy for armchair polyacenes as compared to linear fused polyacenes. Moreover, unlike linear fused polyacenes, the lowest singlet excited state of these oligomers is always found to lie below the lowest dipole forbidden two-photon state indicating that these armchair polyacene oligomers strongly fluoresce. The calculations of low-lying excitations on singly and triply electron doped armchair polyacene oligomers show a low energy band with strong transition dipole moment that coupled to charge conductivity. This implies armchair polyacene posses novel field-effect transistor properties.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Improved renormalization group computation of likelihood functions for cosmological data sets

Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimization and straightforward parallelization.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2011

Imbalanced ultracold Fermi gas in the weakly repulsive regime: Renormalization-group approach for p-wave superfluidity

We theoretically study a possible pairing mechanism for a two-dimensional population imbalanced Fermi gas with short-range repulsive interactions, which can be realized on the upper branch of a Feshbach resonance. We use a well-controlled renormalization-group approach, which allows an unbiased study of the instabilities of imbalanced Fermi liquid without assumption of a broken symmetry and gives a numerical calculation of the transition temperature from microscopic parameters. Our results show a leading superfluid instability in the p-wave channel for the majority species. The corresponding mechanism is that there are effective attractive interactions for the majority species, induced by the particle-hole susceptibility of the minority species, where the mismatch of the Fermi surfaces of the two species plays an important role. We also propose an experimental protocol for detecting the p-wave superfluidity and discuss the corresponding experimental signatures.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Determination of the critical manifold tangent space and curvature with Monte Carlo renormalization group

We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with variational Monte Carlo renormalization group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. Furthermore, we study the isotropic Ising model on square and cubic lattices, the anisotropic Ising model, and the tricritical Ising model on square lattices to illustrate the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2014

Ab initio density matrix renormalization group study of magnetic coupling in dinuclear iron and chromium complexes

The applicability of ab initio multireference wavefunction-based methods to the study of magnetic complexes has been restricted by the quickly rising active-space requirements of oligonuclear systems and dinuclear complexes with S > 1 spin centers. Ab initio density matrix renormalization group (DMRG) methods built upon an efficient parameterization of the correlation network enable the use of much larger active spaces, and therefore may offer a way forward. Here, we apply DMRG-CASSCF to the dinuclear complexes [Fe{sub 2}OCl{sub 6}]{sup 2−} and [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+}. After developing the methodology through systematic basis set and DMRG M testing, we explore the effects of extended active spaces that are beyond the limit of conventional methods. We find that DMRG-CASSCF with active spaces including the metal d orbitals, occupied bridging-ligand orbitals, and their virtual double shells already capture a major portion of the dynamic correlation effects, accurately reproducing the experimental magnetic coupling constant (J) of [Fe{sub 2}OCl{sub 6}]{sup 2−} with (16e,26o), and considerably improving the smaller active space results for [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+} with (12e,32o). For comparison, we perform conventional MRCI+Q calculations and find the J values to be consistent with those from DMRG-CASSCF. In contrast to previous studies, the higher spin states of the two systems show similar deviations from the Heisenberg spectrum, regardless of the computational method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2013

Magnetic transition from the paramagnetic to long-period structure in RMn{sub 2}O{sub 5} multiferroics: Renormalization group analysis of critical behavior

A transition from the paramagnetic state to a long-period magnetic structure with an incommensurate wave vector along one crystallographic axis in RMn{sub 2}O{sub 5} multiferroics is considered. An effective Hamiltonian for these oxides is constructed with allowance for spin fluctuations. Critical points are found, and their stability is analyzed using the renormalization group approach. It is shown that critical fluctuations in these compounds admit a second-order phase transition with respect to a multicomponent order parameter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2018

Holographic heat engines, entanglement entropy, and renormalization group flow

We explore a fruitful connection between the physics of conformal field theories (CFTs) in d-dimensional Minkowski spacetime and the extended gravitational thermodynamics of hyperbolic black holes in (d + 1)-dimensional anti-de Sitter spacetime. The CFTs are reduced on a region bounded by a sphere. We show that renormalization group flows between CFTs are specific thermodynamic processes in the (p,V) plane, where the irreversibility of coarse-graining flows from the ultraviolet to the infrared corresponds to the second law of thermodynamics, preventing heat from flowing from low temperature to high. We observe that holographic heat engines using the black holes as a working substance correspond to specific combinations of CFT flows and deformations. We construct three special engines whose net heat and work can be described in terms of changes of entanglement entropy across the sphere. Engine efficiencies emerge as simple functions of the ratio of the number of degrees of freedom of two CFTs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Revisiting numerical real-space renormalization group for quantum lattice systems

Highlights: •A regularized scheme of the NRG algorithm is proposed. •The method overcomes the boundary obstacle in applying the NRG to quantum lattices. •Extension of the scheme to 2D lattices is illustrated. •Benchmark test on the Heisenberg antiferromagnet demonstrates its numerical validity. -- Abstract: Although substantial progress has been achieved in solving quantum impurity problems, the numerical renormalization group (NRG) method generally performs poorly when applied to quantum lattice systems in a real-space blocking form. The approach was thought to be unpromising for most lattice systems owing to its flaw in dealing with the boundaries of the block. Here the discovery of intrinsic prescriptions to cure interblock interactions is proposed which is able to clear up the boundary obstacle in applying the NRG to quantum lattice systems. While the resulting RG transformation turns out to be strict in the thermodynamic limit, benchmark tests of the algorithm on a one-dimensional Heisenberg antiferromagnet and a two-dimensional tight-binding model demonstrate its numerical efficiency in resolving low-energy spectra for finite lattice systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Topological defect lines and renormalization group flows in two dimensions

We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the ’t Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Renormalization group approach to spinor Bose-Fermi mixtures in a shallow optical lattice

We study a mixture of ultracold spin-half fermionic and spin-one bosonic atoms in a shallow optical lattice where the bosons are coupled to the fermions via both density-density and spin-spin interactions. We consider the parameter regime where the bosons are in a superfluid ground state, integrate them out, and obtain an effective action for the fermions. We carry out a renormalization group analysis of this effective fermionic action at low temperatures, show that the presence of the spinor bosons may lead to a separation of Fermi surfaces of the spin-up and spin-down fermions, and investigate the parameter range where this phenomenon occurs. We also calculate the susceptibilities corresponding to the possible superfluid instabilities of the fermions and obtain their possible broken-symmetry ground states at low temperatures and weak interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗