Search NASA⌕ Search
Home/Archive/DOE OSTI

DOE OSTI · 1029947

Time Evolution with the DMRG Algorithm: A Generic Implementation for Strongly Correlated Electronic Systems

Alvarez, Gonzalo·Dias Da Silva, Luis G·Ponce Mojica, Eduardo M·Dagotto, Elbio R
View original source ↗Export metadata ↓

Abstract

A detailed description of the time-step-targeting time evolution method within the density-matrix renormalization-group algorithm is presented. The focus of this publication is on the implementation of the algorithm and its generic application. The case of one-site excitations within a Hubbard model is analyzed as a test for the algorithm, using open chains and two-leg ladder geometries. The accuracy of the procedure in the case of the recently discussed holon-doublon photo excitations of Mott insulators is also analyzed. Performance and parallelization issues are discussed. In addition, the full open-source code is provided as supplementary material.

Explore related subjects

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSACCURACYALGORITHMSCHAINSDENSITY MATRIXHUBBARD MODELIMPLEMENTATIONPERFORMANCE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alvarez, Gonzalo, Dias Da Silva, Luis G, Ponce Mojica, Eduardo M, Dagotto, Elbio R. 2011-01-01. Time Evolution with the DMRG Algorithm: A Generic Implementation for Strongly Correlated Electronic Systems. https://doi.org/10.1103/physreve.84.056706

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

DOE OSTI2026

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗