SEARCH · Engineering Papers

Results for “numerical 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.

SourceResearch connectionFrom yearThrough year

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

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Continuous-time Monte Carlo renormalization group

We implement the Monte Carlo renormalization group approach in the continuous-time Monte Carlo simulation of a quantum system. In this work, we demonstrate numerically the emergent isotropy between space and time at large distances for the systems that exhibit Lorentz invariance at quantum criticality. Here, this allows us to estimate accurately the sound velocity for these quantum systems. $\textit{Q}$-state Potts models in one and two space dimensions are used to illustrate the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Operator evolution from the similarity renormalization group and the Magnus expansion

The Magnus expansion is an efficient alternative to solving similarity renormalization group (SRG) flow equations with high-order, memory-intensive ordinary differential equation solvers. The numerical simplifications it offers for operator evolution are particularly valuable for in-medium SRG calculations, though challenges remain for difficult problems involving intruder states. Here we test the Magnus approach in an analogous but more accessible situation, which is the free-space SRG treatment of the spurious bound states arising from a leading-order chiral effective field theory (EFT) potential with very high cutoffs. In this work, we show that the Magnus expansion passes these tests and then use the investigations as a springboard to address various aspects of operator evolution that have renewed relevance in the context of the scale and scheme dependence of nuclear processes. These aspects include SRG operator flow with band- versus block-diagonal generators, universality for chiral EFT Hamiltonians and associated operators with different regularization schemes, and the impact of factorization arising from scale separation. Implications for short-range correlations physics and the possibilities for reconciling high- and low-resolution treatments of nuclear structure and reactions are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Dimerization and spin decoupling in a two-leg Heisenberg ladder with frustrated trimer rungs

We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba 4 Ir 3 O 10 . We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong rung coupling a gapped dimerized phase related to competing symmetry sectors in Hilbert space that ultimately results in frustration-driven spin-Peierls transition. In the weak rung-coupling regime, the system is uniform, yet shows a gapped spinon continuum together with a sharp coherent low-energy branch which renders the system critical overall. In either case, the additional rung spin quickly get sidelined and nearly decouple in the regime when their bare coupling to the ladder is weakened

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Ferromagnetism and doublon localization in a Wannier-Hubbard chain

We derive a “Wannier-Hubbard” model consisting of an array of overlapping atomic orbitals interacting via a local Coulomb interaction. Transforming to an orthogonal Wannier basis set, the resulting Hamiltonian displays long-range hopping and interactions, with new terms such as correlated hopping and ferromagnetic direct exchange, among others. We numerically study the one-dimensional version of the model at half-filling using the density matrix renormalization group method, unveiling a rich phase diagram as a function of the interaction U and the overlap s with metallic and ferromagnetic phases separated by a ferrimagnetic region. Our results indicate a path toward understanding emergent phases under pressure and beyond standard model Hamiltonians.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Design, Control and Application of Next Generation Qubits

Design, Control and Application of Next Generation Qubits Arun Bansil, Northeastern University (Principal Investigator) Claudio Chamon, Boston University (Co-Investigator) Adrian Feiguin, Northeastern University (Co-Investigator) Liang Fu, MIT (Co-Investigator) Eduardo Mucciolo, Univ. of Central Florida (Co-Investigator) Qimin Yan, Temple University (Co-Investigator) The quest for developing technologies for manipulating and storing information quantum mechanically is currently led by approaches that include Josephson-junctions, ion-traps, and qubits generated by defect spins in solids. Topological qubits, however, are inherently more robust to decoherence by environmental effects, and should be able to sprint ahead once practical barriers have been overcome. At the present stage of the development of the field, it is important to explore a variety of architectures and materials beyond the conventional paradigms in order to seed breakthroughs toward building a scalable quantum computer. Our comprehensive theoretical research program involved four interconnected thrusts as follows. • A materials discovery effort in two-dimensional compounds in search of materials to support Majorana zero modes and defect structures suitable as qubits. • Exploration of architectures for topological quantum computation by investigating both superconducting Majorana qubits, and robust platforms for braiding with new “meta-materials” built of arrays of Majorana qubits. • Investigation of properties of hybrid metal-organic qubits based on transition-metal centers in graphene, and molecular crystals of polyaromatic complexes with embedded transition-metal atoms. • Development of tensor-network and semiclassical approaches to study decoherence in the presence of random and dispersive spin baths, and NV centers in diamond. The full spectrum of theoretical and numerical approaches was used to address the goals of this project including first-principles, density-matrix-renormalization group, tensor networks, and data-driven high-throughput approaches using materials database and machine-learning.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Entanglement and seniority

In quantum mechanics entanglement is the most striking phenomenon which has no counterpart in classical systems. Although, different approaches have already been developed to study correlations in the case of indistinguishable particles, the exploration of the so-called mode entanglement is still in its initial stage in nuclear physics. Study of mode-entanglement in the seniority model, derivation of analytic formulas for the one-body reduced density matrix of states with seniority $ν$ = 0, 1, 2, and $ν$ = 3, and also determination of the particle number dependence of the one-body reduced density matrix for arbitrary seniority. In addition, comparison of the predictions of the seniority model with the results of the shell model to gain insight into the structure and correlations of the ground and lowest yrast states. In the seniority model the analytic results are calculated using the quasi-spin formalism. The numerical shell model calculations are carried out in the standard shell model framework using an inert core. The applied realistic effective interactions are derived earlier using the $G$-matrix formalism. The density matrix renormalization group method is also applied in order to directly calculate the mode entropies. In the seniority model simple analytical expressions are given for the mode entropies. The peculiar behavior of the half-filled shells and the seniority-zero states are revealed. Numerical results are presented for the lightest stable calcium isotopes and for 94 Ru nucleus. For 94 Ru, the seniority model accounts for the 0$g$ 9/2 mode entropies, but seniority mixing is important for certain yrast states. Furthermore, interaction induced quantum fluctuations decrease the occupation of the 0$f$ 5/2 , 1$p$ 3/2 and 1$p$ 1/2 shells, and amount in non-negligible mode entropies on these shells, too, clearly outside the scope of the simple (0$g$ 9/2 ) 4 seniority model. The 0$f$ 7/2 shell-based seniority model is more accurate for the Ca isotopes, but seniority mixing is substantial for some 44 Ca yrast states, too. Mode and one-body entanglement entropies are useful tools to investigate the structure of quantum correlations in nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Precision study of the massive Schwinger model near quantum criticality

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different “criticality criteria,” observing perfect agreement among them Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

Critical phenomena↗

DOE OSTI2025

Scattering Observables from Few-Body Densities and Compton Scattering on $^6$Li

The dynamics of scattering on light nuclei is numerically expensive using standard methods. Fortunately, recent developments allow one to factor the relevant quantities for a given probe into a convolution of an n -body Transition Density Amplitude (TDA) and the interaction kernel for a given probe. These TDAs depend only on the target, and not the probe; they are calculated once for each set of kinematics and can be used for different interactions.\ % in the same kinematics. The kernels depend only on the probe, and not on the target; they can be reused for different targets and different kinematics. The calculation of TDAs becomes numerically difficult for more than four nucleons, but we discuss a new solution through the use of a Similarity Renormalization Group transformation, and a subsequent back-transformation. This technique allows for extending the TDA method to heavier nuclei such as 6 Li. We present preliminary results for Compton scattering on 6 Li and compare with available data, anticipating an upcoming, more thorough study. We also discuss ongoing extensions to pion-photoproduction and other reactions on light nuclei.

Long, Alexander [George Washington University, Was↗

DOE OSTI2021

Quantum many-body simulations of the two-dimensional Fermi-Hubbard model in ultracold optical lattices

Understanding quantum many-body states of correlated electrons is one main theme in modern condensed-matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, was recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Chen et al., Phys. Rev. X 8, 031082 (2018)], complemented by independent determinant quantum Monte Carlo, offers a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to an unprecedented low temperature of a few percent of the tunneling energy. Finally, we observe excellent agreement with ultracold fermion measurements at both half filling and finite doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behaviors of the antimoments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Tracing the Mott-Hubbard transition in one-dimensional Hubbard models without Umklapp scattering

Here we apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction U equals the bandwidth U c = W, where the single-particle gap opens linearly, Δ(U ≥ W) = U - W. The simple nature of the elementary excitations permits us to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $n_k$ at the Fermi wave number $k_F$ = 0 cannot be used to locate accurately U c from finite-size systems. However, the slope of $n_k$ at the band edges $k_B$ = ±π, reveals the formation of a single-particle bound state which can be used to determine U c reliably from $n_k$ using accurate finite-size data.

1-dimensional systems↗

DOE OSTI2024

Radiative corrections for factorized jet observables in heavy ion collisions

I look at the renormalization of the medium structure function and a medium induced jet function in a factorized cross section for jet substructure observables in Heavy Ion collisions. This is based on the formalism developed in [1], which uses an Open quantum system approach combined with the Effective Field Theory (EFT) for forward scattering to derive a factorization formula for jet observables which work as hard probes of a long lived dilute Quark Gluon Plasma (QGP) medium. I show that the universal medium structure function that captures the observable independent physics of the QGP has both rapidity and UV anomalous dimensions that appear due to medium induced Bremsstrahlung. The resulting Renormalization Group (RG) equations correspond to the BFKL equation and the running of the QCD coupling respectively. I present the first results for the numerical impact of resummation using these RG equations on the mean free path of the jet in the medium. I also briefly discuss the prospects of extending this formalism for a short lived dense medium.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Toward DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: Electrons moving at relativistic speeds, close lying states, and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules in which all the three effects are present. These are the heavier transition metal compounds, lanthanides, and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and the density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs as we demonstrate on the system of TlH, AsH, and SbH.

Brandejs, Jan (ORCID:0000000221073095)↗

DOE OSTI2023

Block2 : A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond

block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.

Chemistry↗

DOE OSTI2020

Two-loop beta function for complex scalar electroweak multiplets

We present the general form of the renormalizable four-point interactions of a complex scalar field furnishing an irreducible representation of SU(2), and derive a set of algebraic identities that facilitates the calculation of higher-order radiative corrections. As an application, we calculate the two-loop beta function for the SM extended by a scalar multiplet, and provide the result explicitly in terms of the group invariants. Our results include the evolution of the Higgs-portal couplings, as well as scalar “minimal dark matter”. We present numerical results for the two-loop evolution of the various couplings.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

On the new universality class in structurally disordered n -vector model with long-range interactions

We study a stability boundary of a region where nontrivial critical behavior of an n-vector model with long-range power-law decaying interactions is induced by the presence of a structural disorder (e.g., weak quenched dilution). This boundary is given by the marginal dimension of the order parameter nc dependent on space dimension, d, and a control parameter of the interaction decay, σ, below which the model belongs to the new dilution-induced universality class. Exploiting the Harris criterion and recent field theoretical renormalization group results for the pure model with long-range interactions, we get nc as a three loop ɛ = 2σ – d-expansion. We provide numerical values for nc applying series resummation methods. Our results show that not only the Ising systems (n = 1) can belong to the new disorder-induced long-range universality class at d = 2 and 3.

Physics↗

DOE OSTI2023

Effective one-band models for the one-dimensional cuprate Ba 2-x Sr x CuO 3+δ

In this work, we consider a multiband Hubbard model H m for Cu and O orbitals in Ba 2-x Sr x CuO 3+δ similar to the three-band model for two-dimensional cuprates. The hopping parameters are obtained from maximally localized Wannier functions derived from ab initio calculations. Using the cell perturbation method, we derive both a generalized t–J model H tJ and a one-band Hubbard model H H to describe the low-energy physics of the system. H tJ has the advantage of having a smaller relevant Hilbert space, facilitating numerical calculations, while additional terms should be included in H H to accurately describe the multiband physics of H m . Using H tJ and the density matrix renormalization group method, we calculate the wave-vector-resolved photoemission and discuss the relevant features in comparison with recent experiments. In agreement with previous calculations, we find that the addition of an attractive nearest-neighbor interaction of the order of the nearest-neighbor hopping shifts the weight from the 3k F to the holon-folding branch. Kinetic effects also contribute to this process.

1-dimensional systems↗

DOE OSTI2023

Ground-state order in magic-angle graphene at filling ν = - 3 : A full-scale density matrix renormalization group study

Here we investigate twisted bilayer graphene (TBG) at filling ν = -3 in the presence of realistic heterostrain. Strain amplifies the band dispersion and drives the system beyond the strong-coupling regime of previous theoretical studies. We use DMRG to conduct an unbiased, large-scale numerical calculations that include all spin and valley degrees of freedom, up to bond dimension χ = 24576. We establish a global phase diagram that unifies a number of theoretical and experimental results. Near zero strain we find an intervalley-coherent quantized anomalous Hall (QAH-IVC) state, a competitive strong-coupling order that evaded past numerical studies. A tiny strain around 0.05% drives a transition into an incommensurate Kekulé spiral (IKS) phase, supporting the mean-field prediction in [Kwan, Phys. Rev. X 11, 041063 (2021)2160-330810.1103/PhysRevX.11.041063]. Even higher strains above 0.2% favor a flavor-symmetric metallic order, which may explain metals found at ν = -3 in many experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Improved coarse-graining methods for two dimensional tensor networks including fermions

We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson-Majorana fermions and for the two flavor Gross-Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher’s zeros.

Phase transitions↗