Session BB04: V: Computational Physics I

Tensor network studies of SrCu2(BO3)2 under pressure and in a magnetic field

The frustrated quantum antiferromagnet SrCu₂(BO₃)₂, which is effectively described by the Shastry-Sutherland model, exhibits a very rich phase diagram as a function of pressure and magnetic field, including an intriguing sequence of magnetization plateaus, several supersolid phases, a finite-temperature critical point, and more. However, its numerical study is very challenging because large parts of the phase diagram are inaccessible by Quantum Monte Carlo due to the negative sign problem. In this talk I will report on recent progress in the accurate study of this model using infinite projected entangled-pair states (iPEPS), a tensor network ansatz to represent states in the 2D thermodynamic limit, and show how it helped to shed new light on the fascinating properties of SrCu₂(BO₃)₂. Based on a recent extension of iPEPS to layered systems, we find that the inclusion of an interlayer coupling leads to a better agreement between experiments and theory regarding the extent of the intermediate plaquette phase.    

All-electron plane-wave electronic structure calculations

We demonstrate the use of the plane wave basis for all-electron electronic structure calculations. The approach relies on the definition of an analytic, norm-conserving, regularized Coulomb potential, and a scalable implementation of the plane wave method capable of handling large energy cutoffs (up to 80kRy in the examples shown). The method is applied to the computation of electronic properties of isolated atoms as well as diamond, silicon, MgO, solid argon, and a configuration of 64 water molecules extracted from a first-principles molecular dynamics simulation [1]. The computed energies, band gaps, ionic forces and stress tensors provide reference results for the validation of pseudopotentials and/or localized basis sets. A calculation of the all-electron band structure of diamond and silicon using the SCAN meta-GGA density functional allows for a validation of calculations based on pseudopotentials derived using the PBE exchange-correlation functional. In the case of (H2O)64, the computed ionic forces provide a reference from which the errors incurred in pseudopotentials calculations and in localized gaussian basis sets calculations can be estimated. All calculations are performed using the Qbox code (http://qboxcode.org).

[1] F. Gygi, J. Chem. Theory Comput. 19, 1300 (2023).   

Scalable higher-order finite-element-based methods for non-collinear magnetism and spin-orbit coupling in real-space density functional theory

We introduce a systematically convergent and scalable higher-order finite-element-based real-space methodology for first-principles calculations of non-collinear magnetic phenomena and spin-orbit coupling effects within pseudopotential Kohn-Sham Density Functional Theory (KS-DFT). Our proposed methodology is compatible with semi-local GGA functionals and utilizes Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials, and accommodates generic boundary conditions, enabling its application to non-periodic, semi-periodic, and fully-periodic systems. Furthermore, we present a generalized configurational force approach for computing atomic forces and periodic cell stresses within the above framework. We subsequently demonstrate the precision and performance of our methodology across diverse benchmark systems involving up to tens of thousands of electrons on multi-node CPU and GPU architectures. Our proposed approach has been integrated into DFT-FE, a massively parallel finite-element-based DFT code.   

Electronic structure and magnetic properties of 3d-substituted double perovskite Bi2NiCrO6

Recently synthesized double perovskite Bi₂NiCrO₆ with Fm-3m structure is investigated with density functional theory calculation using FP-LAPW approach to evaluate its electronic and magnetic properties. The calculation used the Hubbard U parameter (U_eff = 5eV) to account for the localized nature of 3d orbitals that GGA cannot predict correctly. The compound is found to have a Ferromagnetic ground state, and the energy band gap observed in spin up channel and metallic in spin down channel suggests a half-metallic nature with total magnetic moment of 4 μ_B per atomic unit. Further, we studied by substituting a series of 3d elements on Ni and Cr sites on the parent material. Replacing Cr site in the parent compound with Ti, Mn, or Ni, the band gap opening in both spin channels is observed, making them semi-conductors with the energy band gap of 0.581 eV, 0.839 eV, and 0.556 eV respectively. Whereas Cr site was replaced with Co and Zn, half-metallic behavior is observed with a majority contribution of Co-t_2g and Zn-e_g orbitals respectively, in the Fermi level. On substituting Ni site with Mn, Fe, Cu, and Zn are also showed half-metallic behavior with the majority contribution of Cr-t_2g orbitals in the Fermi level. Few of these substituted compounds show ferromagnetic to ferrimagnetic ground state transition. These half-metallic compounds can be good candidates for spintronic devices, and semi-conducting compounds can be good candidates for thermal transistors and phototransistors.   

Real-space finite-element-based methodologies for large-scale ab initio calculations using Projected Augmented Wave (PAW) formalism in density functional theory

Addressing intricate challenges in complex materials problems using ab initio calculation requires significantly large length scales  and longer time scales, demanding enormous computational resources with the current state-of-the-art density functional theory(DFT) codes. Towards this, we introduce systematically convergent and scalable real space finite-element-based methodologies for projector augmented wave (PAW) formalism in DFT. 

 In particular, we propose a local real-space formulation amenable to spectral finite-element discretization of PAW formalism. Subsequently, we develop efficient HPC-centric implementation methodologies combining the ideas of low-rank perturbation of identity and mixed precision arithmetic in conjunction with Chebyshev Filtered subspace iteration approaches to solve the underlying FE discretized PAW generalized eigenproblem. We subsequently benchmark the accuracy and performance of our methodology across diverse benchmark systems involving tens of thousands of electrons on multi-node CPU and GPU architectures. We finally demonstrate that our framework facilitates a substantial reduction in the degrees of freedom to achieve the required chemical accuracy while accommodating generic boundary conditions, thereby enabling faster and more accurate large-scale DFT simulations than possible today.   

Environment expansion for Matrix Product State and Tensor Network methods

We present a method for incorporating degrees of freedom into bonds of a tensor network inspired by single-site density matrix mixing schemes and the single-site subspace expansion (3S) algorithm. This is applicable in a wide range of scenarios and we will present some benchmarks for various Matrix Product State algorithms including DMRG, TDVP, and Excitation Ansatz. The Environment Expansion approach is a simple and effective way to control bond dimension expansion, and will likely become a standard part of the MPS 'toolbox'.   

Well-posed equations of motion for charged fluids in general relativity

In general relativity, including electric charge in fluid problems results in underdetermined equations: there are only 3 dynamical equations of motion, but there are 6 dynamic degrees of freedom: 3 in the fluid and 3 in the electromagnetic (EM) current. In the literature, families of solutions are found as functions of the left-over degrees of freedom, which must be fixed to find solutions.

In this talk, additions to the EM stress-energy tensor are presented that are quadratic in the EM 4-current. With no extra fluid, there are the same number of equations as unknowns. Not all quadratic, symmetric combinations of the EM current are compatible with the EM stress-energy tensor; to satisfy both momentum and energy conservation, the scalar product of the EM current and divergence of the stress-energy tensor must be zero. The only compatible stress-energy tensor quadratic in the EM current is equivalent to that of a polytropic fluid with adiabatic exponent of 2, and negligible rest mass density (and is also equivalent to the addition in Bopp-Podolsky EM). This stress-energy tensor can be found by varying a Lagrangian  quadratic the EM current. We also present two other independent Lagrangians that are quadratic in the first derivative of the EM field tensor; one violates parity and is zero in flat space-time, and the other reduces to the first Lagrangian in flat space-time.

We find static solutions in spherical symmetry, which have infinite central density, consistent with previously published results.   

The Physical Universes as the Equivalency Classes Embedded in Universal Machinery Networks: On the Possibility of Physically Phantom Universes

The inflective single point space¹ provides explaining what things govern the Natural Principles, NPs in Naturally Physical Universes, NPUs through Equivalency Control Mechanisms, ECMs. The inflective balls structures in Topological Universes, TUs bring the facilities of Embedded Filtering and Modulating Activities, EFaMAs on the metrics of corresponding PUs. This possibility comes by applying Time Energy¹, t^E in field equations and converting them to state equations in circuits and networks². The approach provides considering TUs as equivalency classes embedded in Universal Machinery Network, UMN. The naturally EFaMAs embed self-detectable topological structures in NPUs and interpret them as NPU’s MN. The t^E plays carrier role while Time Span, t^s is transmitted signal. The Modulation Operator, MO generates t^s from t^E. The inverse of MO may interfere with t^s in some conditions. The interference through MO may bring separate but non-permanent PUs, say phantom TUs, in NPUs. The approach gives a method of complete invisibility for physical things in NPUs through self-EFaMAs.

The NPs and ECMs can work as detectability and observability conditions iff they are self-EFaMAs.

¹ doi:10.23919/URSIGASS51995.2021.9560637.

² https://www.piers.org/pierspublications/PIERS2013StockholmAbstracts.pdf.