Next generation multi-scale quantum simulations for strongly correlated materials

This thesis represents our effort to develop the next generation multi-scale quantum simulation methods suitable for strongly-correlated materials, where complicated phase-diagrams prevail, suggesting complicated underlying physics. We first give a detailed description of the parquet formalism. With its help, different approximate methods can be unified and a hierarchy of approximate methods with different accuracies and computational complexity can thus be designed. Next, we present a numerical solution of the parquet approximation. Results on the Hubbard model are compared to those obtained from Determinant Quantum Monte Carlo (DQMC), FLuctuation EXchange (FLEX), and self-consistent second-order approximation methods. The comparison shows a satisfactory agreement with DQMC and a significant improvement over the FLEX or the self-consistent second-order approximation. The parquet formalism can also be used to analyze the superconducting mechanism of the high-temperature superconductors. The dynamical cluster approximation (DCA) method is used to understand the proximity of the superconducting dome to the quantum critical point in the 2-D Hubbard model. At optimal doping, where Vd is revealed to be featureless, we find a power-law behavior of chi_0d(w=0), replacing the BCS logarithm behavior, and strongly enhanced T_c. After that we propose another multi-scale approach by combining the DCA and the recently introduced dual-fermion formalism. Within this approach, short and long length scale physics is addressed by the DCA cluster calculation, while intermediate length scale physics is addressed diagrammatically using dual fermions. The bare and dressed dual fermionic Green functions scale as O(1/Lc), so perturbation theory on the dual lattice converges very quickly. Lastly, we study the responses to dynamical modulation of the optical lattice potential by analyzing properties of the repulsive fermionic Hubbard model in an optical lattice. We provide numerical evidence showing the modulations by on-site local interaction cannot be ignored, and instead can even strongly contribute to the dynamical behaviors of the system in highly-doped cases

Probabilistic threshold range aggregate query processing over uncertain data

Uncertainty is inherent in many novel and important applications such as market surveillance, information extraction sensor data analysis, etc. In the recent a few decades, uncertain data has attracted considerable research attention. There are various factors that cause the uncertainty, for instance randomness or incompleteness of data, limitations of equipment and delay or loss in data transfer. A probabilistic threshold range aggregate (PRTA) query retrieves summarized information about the uncertain objects in the database satisfying a range query, with respect to a given probability threshold. This thesis is trying to address and handle this important type of query which there is no previous work studying on. We formulate the problem in both discrete and continuous uncertain data model and develop a novel index structure, asU-tree (aggregate-based sampling-auxiliary U-tree) which not only supports exact query answering but also provides approximate results with accuracy guarantee if efficiency is more concerned. The new asU-tree structure is totally dynamic. Query processing algorithms for both exact answer and approximate answer based on this new index structure are also proposed. An extensive experimental study shows that asU-tree is very efficient and effective over real and synthetic datasets

Dynamics of the Geometric Phase in Inhomogeneous Quantum Spin Chains

The dynamics of the geometric phase are studied in inhomogeneous quantum spin chains after a quench. Analytic expressions of the Pancharatnam geometric phase (PGP) $\mathcal{G}(t)$ are derived, for both the period-two quantum Ising chain (QIC) and the disordered QIC. In the period-two QIC, due to the periodic modulation, the PGP changes with time at the boundary of the Brillouin zone, and consequently, the winding number $\nu_{D}(t)=\int_{0}^{\pi}[\partial\phi_{k}^{G}(t)/\partial k]dk/2\pi$ based on the PGP is not quantized and thus not topological anymore. Nevertheless, the PGP and its winding number show non-analytic singularities at the critical times of the dynamical quantum phase transitions (DQPTs). This relation between the PGP and the DQPT is further confirmed in the disordered QIC, where the winding number is not defined. It is found that the critical time of DQPT inherited from the homogeneous system and the additional one induced by the weak disorder are also accompanied by the non-analytic singularity of the PGP, by decomposing the PGP into each quasiparticle mode. The connection between the non-analytic behavior of the PGP at the critical time and the DQPT, regardless of whether the winding number is topological, can be explained by the fact that they both arise when the Loschmidt amplitude vanishes.Comment: 14 pages, 8 figure

Periodic Anderson model with Holstein phonons for the description of the Cerium volume collapse

Recent experiments have suggested that the electron-phonon coupling may play an important role in the $\gamma \rightarrow \alpha$ volume collapse transition in Cerium. A minimal model for the description of such transition is the periodic Anderson model. In order to better understand the effect of the electron-phonon interaction on the volume collapse transition, we study the periodic Anderson model with coupling between Holstein phonons and electrons in the conduction band. We find that the electron-phonon coupling enhances the volume collapse, which is consistent with experiments in Cerium. While we start with the Kondo Volume Collapse scenario in mind, our results capture some interesting features of the Mott scenario, such as a gap in the conduction electron spectra which grows with the effective electron-phonon coupling.Comment: 8 pages, 6 figure

Determinative developmental cell lineages are robust to cell deaths

All forms of life are confronted with environmental and genetic perturbations, making phenotypic robustness an important characteristic of life. Although development has long been viewed as a key component of phenotypic robustness, the underlying mechanism is unclear. Here we report that the determinative developmental cell lineages of two protostomes and one deuterostome are structured such that the resulting cellular compositions of the organisms are only modestly affected by cell deaths. Several features of the cell lineages, including their shallowness, topology, early ontogenic appearances of rare cells, and non-clonality of most cell types, underlie the robustness. Simple simulations of cell lineage evolution demonstrate the possibility that the observed robustness arose as an adaptation in the face of random cell deaths in development. These results reveal general organizing principles of determinative developmental cell lineages and a conceptually new mechanism of phenotypic robustness, both of which have important implications for development and evolution

Leading components and pressure-induced color changes in N-doped lutetium hydride

Recent experimental study by Dias {\it et al.} claims to have discovered room-temperature superconductivity in lutetium-nitrogen-hydrogen system at 1 GPa [Nature 615, 244 (2023)], which sheds light on the long-held dream of ambient superconductivity. However, all follow-up experiments found no evidence of superconductivity. The compositions and the crystal structures of the lutetium-nitrogen-hydrogen system remain unknown. By employing the density functional theory based structure prediction algorithm, we suggest that in lutetium-nitrogen-hydrogen the major component is LuH$_2$ (Fm$\bar{3}$m), together with minor LuN (Fm$\bar{3}$m). The blue LuH$_2$ at ambient pressure will turn into purple and red color at higher pressures, possibly accompanied by the formation of vacancies at hydrogen-sites. In LuH$_2$ and LuN, the density of states at the Fermi level is dominated by the Lu-5d orbitals, while those from hydrogen and nitrogen are very small, leading to the absence of superconductivity in these two compounds. Nitrogen-doping to LuH$_2$ fails to enhance the superconductivity as well. In this work, we identify the leading components in N-doped lutetium hydride, explain its intriguing color changes under pressure, and elucidate why superconductivity is absent in the follow-up experiments

CAS9 is a genome mutator by directly disrupting DNA-PK dependent DNA repair pathway.

With its high efficiency for site-specific genome editing and easy manipulation, the clustered regularly interspaced short palindromic repeats (CRISPR)/ CRISPR associated protein 9 (CAS9) system has become the most widely used gene editing technology in biomedical research. In addition, significant progress has been made for the clinical development of CRISPR/CAS9 based gene therapies of human diseases, several of which are entering clinical trials. Here we report that CAS9 protein can function as a genome mutator independent of any exogenous guide RNA (gRNA) in human cells, promoting genomic DNA double-stranded break (DSB) damage and genomic instability. CAS9 interacts with the KU86 subunit of the DNA-dependent protein kinase (DNA-PK) complex and disrupts the interaction between KU86 and its kinase subunit, leading to defective DNA-PK-dependent repair of DNA DSB damage via non-homologous end-joining (NHEJ) pathway. XCAS9 is a CAS9 variant with potentially higher fidelity and broader compatibility, and dCAS9 is a CAS9 variant without nuclease activity. We show that XCAS9 and dCAS9 also interact with KU86 and disrupt DNA DSB repair. Considering the critical roles of DNA-PK in maintaining genomic stability and the pleiotropic impact of DNA DSB damage responses on cellular proliferation and survival, our findings caution the interpretation of data involving CRISPR/CAS9-based gene editing and raise serious safety concerns of CRISPR/CAS9 system in clinical application

The response to dynamical modulation of the optical lattice for fermions in the Hubbard model

Fermionic atoms in a periodic optical lattice provide a realization of the single-band Hubbard model. Using Quantum Monte Carlo simulations along with the Maximum Entropy Method, we evaluate the effect of a time-dependent perturbative modulation of the optical lattice amplitude on atomic correlations, revealed in the fraction of doubly-occupied sites. Our treatment extends previous approaches which neglected the time dependence of the on-site interaction, and shows that this term changes the results in a quantitatively significant way. The effect of modulation depends strongly on the filling-- the response of the double occupation is significantly different in the half-filled Mott insulator from the doped Fermi liquid region.Comment: 4 pages, 4 figure