Related papers: Derivation of the Ghost Gutzwiller Approximation f…
By combining classical Monte Carlo and Bethe ansatz techniques we devise a numerical method to construct the Truncated Generalized Gibbs Ensemble (TGGE) for the spin-1/2 isotropic Heisenberg ($XXX$) chain. The key idea is to sample the…
Identifying variational wave functions that efficiently parametrize the physically relevant states in the exponentially large Hilbert space is one of the key tasks towards solving the quantum many-body problem. Powerful tools in this…
We present a theory of ghost-free massive gravity where the mass of the graviton is generated through the Brout-Englert-Higgs (BEH) mechanism and one of the four scalar fields used is that of mimetic gravity. The mass term is not of the…
We introduce a novel approach to improve unsupervised hashing. Specifically, we propose a very efficient embedding method: Gaussian Mixture Model embedding (Gemb). The proposed method, using Gaussian Mixture Model, embeds feature vector…
We investigate fundamental properties of meta-generalized-gradient approximations (meta-GGAs) to the exchange-correlation energy functional, which have an implicit density dependence via the Kohn-Sham kinetic-energy density. To this…
Successful modern generalized gradient approximations (GGA) are biased toward atomic energies. Restoration of the first-principles gradient expansion for the exchange energy over a wide range of density gradients eliminates this bias. We…
We explicitly build a generalized local-density approximation (GLDA) correlation functional based on one-dimensional (1D) uniform electron gases (UEGs). The fundamental parameters of the GLDA \textemdash a generalization of the widely-known…
Density matrix embedding theory (DMET) is a powerful quantum embedding method for solving strongly correlated quantum systems. Theoretically, the performance of a quantum embedding method should be limited by the computational cost of the…
Gutzwiller's semiclassical trace formula for the density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these…
The exact one-loop beta functions for the four-derivative terms (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet) are derived for the minimal six-derivative quantum gravity (QG) theory in four spacetime dimensions. The…
Density functional theory (DFT) has transformed our ability to investigate and understand electronic ground states. In its original formulation, however, DFT is not suited to addressing (e.g.) degenerate ground states, mixed states with…
We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation…
We derive expressions required in generalizing the Gutzwiller approximation to models comprising arbitrarily degenerate localized orbitals.
We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard-Holstein model, which is paradigmatic for the interplay of electron-electron and electron-phonon interactions. Analyzing the single-particle excitation…
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing…
We use the Gaussian variational principle to apply cMERA to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a correspondence between the first two terms in the variational expansion and the Gaussian…
This thesis explores the cosmological implications of modified gravity, focusing on nonmetricity-based $f(Q)$ gravity as an alternative to the $\Lambda$CDM model in explaining cosmic acceleration. Chapter I lays the theoretical groundwork…
We revisit ghost dark matter, the possibility that ghost condensation may serve as an alternative to dark matter. In particular, we investigate the Friedmann-Robertson-Walker (FRW) background evolution and the large-scale structure (LSS) in…
We present a finite-temperature extension of density matrix embedding theory (FT-DMET) for realistic crystalline systems. We describe a practical framework for constructing extended bath orbitals, solving the embedding problem, and…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…