Related papers: Linear-time generalized Hartree-Fock algorithm for…
We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes the Wang-Landau algorithm to quantum systems with continuous degrees of freedom, to the fermionic Hubbard model with repulsive interactions on the honeycomb lattice.…
Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Efficient computation of molecular integrals and Hartree-Fock energy remains a central topic in quantum-chemistry algorithm development. Although many sophisticated open-source packages are available, understanding their implementations…
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in…
Repeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimizations. While many efficient…
A new method of calculating pairing correlations in coordinate space with finite range interactions is presented. In the Hartree-Fock-Bogoliubov (HFB) approach the mean field part is derived from a Skyrme-type force whereas the pairing…
We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input…
Even after almost a century, the foundations of quantum statistical mechanics are still not completely understood. In this work, we provide a precise account on these foundations for a class of systems of paradigmatic importance that appear…
Using a combination of results from exact mappings and from mean-field theory we explore the phase diagram of quasi-one-dimensional systems of identical fermions with attractive dipolar interactions. We demonstrate that at low density these…
This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
Continuous-time determinantal algorithm is proposed for the quantum Monte Carlo simulation of the interacting fermions. The scheme does not invoke Hubbard-Stratonovich transformation. The fermionic action is divided into two parts. One of…
Efficient continuous time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state-of-the-art for most discrete quantum models. They have not been widely used yet for fermionic quantum…
The time-dependent Hartree-Fock equations are derived from the N-particle Schr\"odinger equation with mean-field scaling in the infinite particle limit, for initial data that are like Slater determinants. Only the case of bounded…
We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an…
We analyze a class of mean-field (MF) lattice-fermion Hamiltonians and construct the corresponding grand-canonical density operator for such system. New terms are introduced, which may be interpreted as local fugacities, molecular fields,…
We combine matrix-product state (MPS) and Mean-Field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between…
We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix…
Recent progress in mathematical theory of random processes provides us with non-Fock product systems (continuous tensor products of Hilbert spaces) used here for constructing a toy model for fermions. Some state vectors describe infinitely…