Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is found that best results can be achieved using a flexible GMRES solver for matrix inversions and the second order Omelyan integrator with Hasenbusch acceleration on different time scales for molecular dynamics. We demonstrate how an arbitrary number of Hasenbusch mass terms can be included into this geometry and find that the optimal speed depends weakly on the choice of the number of Hasenbusch masses and their values. As such, the tuning of these masses is amenable to automization and we present an algorithm for this tuning that is based on the knowledge of the dependence of solver time and forces on the Hasenbusch masses. We benchmark our algorithms to systems where direct numerical diagonalization is feasible and find excellent agreement. We also simulate systems with hexagonal lattice dimensions up to $102\times 102$ and $N_t=64$. We find that the Hasenbusch algorithm leads to a speed up of more than an order of magnitude.Comment: Corrected Proof in Press in Computer Physics Communication

The Semimetal-Antiferromagnetic Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice

The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well as the critical exponents $\nu=1.181(43)$ and $\beta=0.898(37)$ which are expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits, and perform a data collapse fit. We also determine the zero temperature values of single particle gap and staggered magnetisation on both sides of the phase transition.Comment: LATTICE2021 proceedings, more details in arXiv:2005.11112 and arXiv:2105.0693

The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice

We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/\kappa=3.834(14)$ and the critical exponent $z\nu=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $\beta=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators

Recent progress in the JARVIS infrastructure for next-generation data-driven materials design

The Joint Automated Repository for Various Integrated Simulations (JARVIS) infrastructure at the National Institute of Standards and Technology (NIST) is a large-scale collection of curated datasets and tools with more than 80000 materials and millions of properties. JARVIS uses a combination of electronic structure, artificial intelligence (AI), advanced computation and experimental methods to accelerate materials design. Here we report some of the new features that were recently included in the infrastructure such as: 1) doubling the number of materials in the database since its first release, 2) including more accurate electronic structure methods such as Quantum Monte Carlo, 3) including graph neural network-based materials design, 4) development of unified force-field, 5) development of a universal tight-binding model, 6) addition of computer-vision tools for advanced microscopy applications, 7) development of a natural language processing tool for text-generation and analysis, 8) debuting a large-scale benchmarking endeavor, 9) including quantum computing algorithms for solids, 10) integrating several experimental datasets and 11) staging several community engagement and outreach events. New classes of materials, properties, and workflows added to the database include superconductors, two-dimensional (2D) magnets, magnetic topological materials, metal-organic frameworks, defects, and interface systems. The rich and reliable datasets, tools, documentation, and tutorials make JARVIS a unique platform for modern materials design. JARVIS ensures openness of data and tools to enhance reproducibility and transparency and to promote a healthy and collaborative scientific environment