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We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum…
Linear response theories in the continuum capable of describing continuum spectra and dynamical correlations are presented. Our formulation is essentially the same as the continuum random-phase approximation (RPA) but suitable for uniform…
We explore the two-dimensional extended Hubbard model on the triangular lattice in the high doping regime. On-site and nearest-neighbour repulsive interactions are treated in a non-perturbative way by means of Extended Dynamical Mean Field…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
We study the properties of the ground states of the one- and two-dimensional Hubbard models at half filling and moderate doping using entanglement-based measures, which we calculate numerically using the momentum-space density matrix…
We study the intricate relationships between the dynamical scaling properties of electron wave packets and the multifractality of the eigenstates in quantum systems. Numerical simulations for the Harper model and the Fibonacci chain…
Employing large-scale quantum Monte Carlo simulations, we systematically compute the energy spectra of the 2D spin-1/2 Heisenberg model with long-range interactions. With the $1/r^{\alpha}$ ferromagnetic and staggered antiferromagnetic…
We propose a $\Gamma$-convergent discrete approximation of the Mumford-Shah functional. The discrete functionals act on functions defined on stationary stochastic lattices and take into account general finite differences through a…
Accurate exchange-correlation (XC) potentials are essential for density functional theory, yet reliable approximations remain challenging for strongly correlated systems. In this work, we present a quantum algorithmic framework to determine…
Magnetic and electronic properties of the Hubbard model on the Bethe and fcc lattices in infinite dimensions have been investigated numerically on the basis of the dynamical coherent potential approximation (CPA) theory combined with the…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
This thesis surveys the research in patch-based synthesis and algorithms for finding correspondences between small local regions of images. We additionally explore a large kind of applications of this new fast randomized matching technique.…
When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…
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…
We present an elegant and simple dynamical model of symmetric, non-degenerate (n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic lattice with nearest-neighbor interactions. We show how this model is related to…
The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence…
We formulate a set of equations that facilitate an exact numerical solution of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour hopping and arbitrary site potentials. The approach relies on a mapping of the…
The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…
We review recent developments in electronic structure calculations that go beyond state-of-the-art methods such as density functional theory (DFT) and dynamical mean field theory (DMFT). Specifically, we discuss the following methods: GW as…