Thermodynamic prediction of glass formation tendency, cluster-in-jellium model for metallic glasses, ab initio tight-binding calculations, and new density functional theory development for systems with strong electron correlation

We have calculated the T0 curves for several Al-Rare Earth (RE) binary alloys and compared the results with reported observations of glass formation (T0 curve is defined as a trajectory in temperature-composition space where the liquid phase and solid phase have same Gibbs free energies), in order to assess the importance of the transport-based resistance to crystallization in the overall glass formation process. Our results show that the experimentally observed glass forming compositions for Al-(Ce,Gd,Ho,Nd,Y,Dy) alloys strongly correlate with the composition range bounded by the T0 curves associated with the relevant crystalline phases. This agreement indicates that sluggish material transport is a key factor governing glass formation in these systems, a behavior that differs substantially from the more common oxide glasses, where directional bonding constraints may stabilize the glassy network based on topological considerations. A jellium-passivated cluster model is developed to study the energetics of short-range ordering in supercooled liquid and glass systems. Calculations for single atoms embedded in jellium yield results in good agreement with bulk values for the cohesive energy, atomic volume as well as angular-momentum-projected electronic density of states. The energy difference between icosahedral clusters and FCC embryos in jellium is found to correlate with the glass-forming ability of liquid Al alloys. The model will be useful for studying the short-range order tendency with minor chemical additions in metallic glass formation, without the use of large unit cell calculations. We demonstrate an efficient and accurate first-principles method to calculate the electronic structure of a large system using a divide-and-conquer strategy based on localized quasi-atomic minimal basis set orbitals recently developed. Tight-binding Hamiltonian and overlap matrices of a big system can be constructed by extracting the matrix elements for a given pair of atoms from first-principles calculations of smaller systems that represent the local bonding environment of the particular atom pair. The approach is successfully applied to the studies of electronic structure in graphene nano-ribbons. This provides a promising way to do the electronic simulation for big systems directly from first-principles. We have developed a new density functional theory incorporating the correlated electronic effects into the kinetic energy via Gutzwiller approximation. All the Coulomb integrals are determined self-consistently without any adjustable parameters. In addition to the set of one-electron Schrydinger equations analogous to the standard LDA approach, we get another set of linear equations with respect to the probabilities of local configurations as the solution of the many body problem. A preliminary Fortran90 code has been developed with an interface to VASP. We applied our method to several systems with important electron correlation effects and got encouraging results

Principle of maximum entanglement entropy and local physics of strongly correlated materials

We argue that, because of quantum entanglement, the local physics of strongly correlated materials at zero temperature is described in a very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number of local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits and present numerical calculations of the iron compounds FeSe and FeTe and of the elemental cerium by employing the Gutzwiller approximation that strongly support our theory in general

Thermodynamic limits of crystallization and the prediction of glass formation tendency

We have calculated the T0 curves for several Al-rare-earth binary alloys to assess the importance of the transport-based resistance to crystallization in the overall glass formation process and the general effectiveness of thermodynamic prediction of glass-forming ability. Our results show that the experimentally observed glass-forming compositions for Al-(Ce, Gd, Ho, Nd, Y, Dy) alloys strongly correlate with the composition range bounded by the T0curves associated with the relevant crystalline phases. This indicates that sluggish material transport, together with the tendency for clustering and other types of ordering at medium-range scale, is a key factor governing glass formation in these systems

Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials

Rapid progress in noisy intermediate-scale quantum (NISQ) computing technology has led to the development of novel resource-efficient hybrid quantum-classical algorithms, such as the variational quantum eigensolver (VQE), that can address open challenges in quantum chemistry, physics and material science. Proof-of-principle quantum chemistry simulations for small molecules have been demonstrated on NISQ devices. While several approaches have been theoretically proposed for correlated materials, NISQ simulations of interacting periodic models on current quantum devices have not yet been demonstrated. Here, we develop a hybrid quantum-classical simulation framework for correlated electron systems based on the Gutzwiller variational embedding approach. We implement this framework on Rigetti quantum processing units (QPUs) and apply it to the periodic Anderson model, which describes a correlated heavy electron band hybridizing with non-interacting conduction electrons. Our simulation results quantitatively reproduce the known ground state quantum phase diagram including metallic, Kondo and Mott insulating phases. This is the first fully self-consistent hybrid quantum-classical simulation of an infinite correlated lattice model executed on QPUs, demonstrating that the Gutzwiller hybrid quantum-classical embedding framework is a powerful approach to simulate correlated materials on NISQ hardware. This benchmark study also puts forth a concrete pathway towards practical quantum advantage on NISQ devices.Comment: 14 pages, 5 figure

Active learning approach to simulations of strongly correlated matter with the ghost Gutzwiller approximation

Quantum embedding (QE) methods such as the ghost Gutzwiller approximation (gGA) offer a powerful approach to simulating strongly correlated systems, but come with the computational bottleneck of computing the ground state of an auxiliary embedding Hamiltonian (EH) iteratively. In this work, we introduce an active learning (AL) framework integrated within the gGA to address this challenge. The methodology is applied to the single-band Hubbard model and results in a significant reduction in the number of instances where the EH must be solved. Through a principal component analysis (PCA), we find that the EH parameters form a low-dimensional structure that is largely independent of the geometric specifics of the systems, especially in the strongly correlated regime. Our AL strategy enables us to discover this low-dimensionality structure on the fly, while leveraging it for reducing the computational cost of gGA, laying the groundwork for more efficient simulations of complex strongly correlated materials

Efficient Step-Merged Quantum Imaginary Time Evolution Algorithm for Quantum Chemistry

We develop a resource-efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine the binding energy curves of a set of molecules, including H2, H4, H6, LiH, HF, H2O, and BeH2, and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional nonconvex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum devices