Accurately computing excited states and lattice dependent tight-binding models from first principles simulations

The core problem of condensed matter physics is the understanding of how diverse macroscopic quantum phenomenon can emerge from a basic set of constituent particles and their interactions. Fortunately, quantum mechanics provides a universal bridge between the microscopic electrons and macroscopic quantum phenomenon via the ab initio Hamiltonian and Hilbert space. The eigenstates and eigenenergies of the ab initio Hamiltonian exactly correspond to the excited states and energies of a given material, and can be used to compute physical observables like conductivity, optical gaps, and magnetization. However, computing the eigenstates and eigenspectrum of the ab initio Hamiltonian through brute force methods is generally computationally intractable, except in special cases of small molecules like H2. Instead, approximate methods have been developed and used to great success in accurately computing the eigenspectrum and eigenstates of the ab initio Hamiltonian, falling under the categories of first principles methods and effective model Hamiltonians. While both first principles methods and effective model Hamiltonians have been used to accurately compute properties of real materials, significant avenues of research still remain. The biggest avenue for discovery is first principles excited states methods, with accurate ground state techniques like quantum Monte Carlo lacking a mature excited state counterpart. Accompanying this large avenue for change is the constant need for adaptation and development of methods to keep up with the rapid rate of novel materials discoveries. The construction of interacting effective Hamiltonians from ab initio calculations is the predominant challenge in the effective model approach. To this end, my thesis has been oriented around advancing the state of the art in first principles excited state computation and effective models with lattice effects. First, I present my work on investigating a new trial wave function for use in quantum Monte Carlo (QMC). The new non-orthogonal determinant wave function expands the possibilities of accurate QMC calculations, as the quality of the trial wave function is a primarily limiting factor of accuracy in QMC calculations. Next, I present my work on developing a stable statistical estimate for gradients used in QMC wave function optimization. This efficient method is simple to integrate into existing QMC codes, and improves the efficiency of QMC wave function optimization, an integral component of QMC calculations. Following that, I present my work on creating a novel method for computing excited states in QMC. The novel method addresses short comings of state-of-the-art QMC methods by allowing for state specific optimization with high accuracy and computational efficiency. I conclude by demonstrating my work building a tight-binding model for twisted bilayer graphene with lattice interactions from density functional theory (DFT). The work provided a pipeline for developing accurate DFT models with electron-lattice interaction, and demonstrated the importance of these interactions in the quantitative and qualitative description of the flat bands in magic angle TBLG. My work demonstrates the power of ab initio techniques in accurately computing excitations and eigenstates of complex quantum systems, and provides a concrete stepping stone towards the ad- vancement of accurate and efficient first principles methods and effective model Hamiltonians

A Compact Reconfigurable Multi-mode Resonator-based Multi-band Band Pass Filter for Intelligent Transportation Systems Applications

A compact wide band reconfigurable bandpass filter (BPF) which utilises a hemi-circular flower shaped multimode resonator (MMR) is presented. The proposed MMR provides three resonant modes which fall within the broad frequency spectra. Among these, two modes are even and one is odd. These modes are optimised by varying the dimensions so as to obtain the desired frequency response. The fractional bandwidth is more than 96 per cent. The filter can be operated as multi-band BPF. In OFF condition of ‘Pin’ diode, the centre frequencies are 2.43 GHz, 3.5 GHz, and 5.9 GHz in ON condition of ‘Pin’ diode centre frequencies are 2.43 GHz, 3.5 GHz, 5.9 GHz, 6.5 GHz, and 8.8 GHz which are used for vehicular, WiMAX, intelligent transportation systems and satellite communication respectively. Microstrip filter structures are integrated with ‘Pin’ diodes. Appropriate biasing has been provided by choosing lumped components with precise values. The insertion loss in OFF condition are 0.5 dB, 0.67 dB, and 0.8 dB and in ON condition 0.5 dB, 0.7 dB, 1.2 dB, and 1.9 dB. The measured results agree well with the full-wave simulated results

When is better ground state preparation worthwhile for energy estimation?

Many quantum simulation tasks require preparing a state with overlap $\gamma$ relative to the ground state of a Hamiltonian of interest, such that the probability of computing the associated energy eigenvalue is upper bounded by $\gamma^2$. Amplitude amplification can increase $\gamma$, but the conditions under which this is more efficient than simply repeating the computation remain unclear. Analyzing Lin and Tong's near-optimal state preparation algorithm we show that it can reduce a proxy for the runtime of ground state energy estimation near quadratically. Resource estimates are provided for a variety of problems, suggesting that the added cost of amplitude amplification is worthwhile for realistic materials science problems under certain assumptions

Design of RF Receiver Front end Subsystems with Low Noise Amplifier and Active Mixer for Intelligent Transportation Systems Application

This paper presents the design, simulation, and characterization of a novel low-noise amplifier (LNA) and active mixer for intelligent transportation system applications. A low noise amplifier is the key component of RF receiver systems. Design, simulation, and characterization of LNA have been performed to obtain the optimum value of noise figure, gain and reflection coefficient. Proposed LNA achieves measured voltage gains of ~18 dB, reflection coefficients of -20 dB, and noise figures of ~2 dB at 5.9 GHz, respectively. The active mixer is a better choice for a modern receiver system over a passive mixer. Key sight advanced design system in conjunction with the electromagnetic simulation tool, has been to obtain the optimal conversion gain and noise figure of the active mixer. The lower and upper resonant frequencies of mixer have been obtained at 2.45 GHz and 5.25 GHz, respectively. The measured conversion gains at lower and upper frequencies are 12 dB and 10.2 dB, respectively. The measured noise figures at lower and upper frequencies are 5.8 dB and 6.5 dB, respectively. The measured mixer interception point at lower and upper frequencies are 3.9 dBm and 4.2 dBm

Registry-dependent potential energy and lattice corrugation of twisted bilayer graphene from quantum Monte Carlo

An uncertainty in studying twisted bilayer graphene (TBG) is the minimum energy geometry, which strongly affects the electronic structure. The minimum energy geometry is determined by the potential energy surface, which is dominated by van der Waals (vdW) interactions. In this work, large-scale diffusion quantum Monte Carlo (QMC) simulations are performed to evaluate the energy of bilayer graphene at various interlayer distances for four stacking registries. An accurate registry-dependent potential is fit to the QMC data and is used to describe interlayer interactions in the geometry of near-magic-angle TBG. The band structure for the optimized geometry is evaluated using the accurate local-environment tight-binding model. We find that compared to QMC, DFT-based vdW interactions can result in errors in the corrugation magnitude by a factor of 2 or more near the magic angle. The error in corrugation then propagates to the flat bands in twisted bilayer graphene, where the error in corrugation can affect the bandwidth by about 30% and can change the nature and degeneracy of the flat bands

PyQMC: an all-Python real-space quantum Monte Carlo module in PySCF

We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or “quakes”. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects “tuned critical” behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes

Building an ab initio solvated DNA model using Euclidean neural networks

Accurately modeling large biomolecules such as DNA from first principles is fundamentally challenging due to the steep computational scaling of ab initio quantum chemistry methods. This limitation becomes even more prominent when modeling biomolecules in solution due to the need to include large numbers of solvent molecules. We present a machine learning electron density model based on a Euclidean neural network framework to model explicitly solvated double-stranded DNA. The neural network framework has a built-in understanding of equivariance, allowing the model to learn 3D structural information efficiently by exploiting the properties of Euclidean symmetry. By training the machine learning model using molecular fragments that sample the key DNA and solvent interactions, we show that the model predicts electron densities of arbitrary systems of solvated DNA accurately, resolves polarization effects that are neglected by classical force fields, and captures the physics of the DNA-solvent interaction at the ab initio level