Related papers: Shifted COCG method and its application to double …
We developed a fast numerical methodfor complex symmetric shifted linear systems, which is motivated by the quantum-mechanical (electronic-structure) theory in nanoscale materials. The method is named shifted Conjugate Orthogonal Conjugate…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
Self-consistent approaches to superfluid many-fermion systems in 3-dimensions (and subsequent time-dependent approaches) require a large number of diagonalizations of very large dimension hermitian matrices, which results in enormous…
We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…
Ground state properties of multi-orbital Hubbard models are investigated by the auxiliary field quantum Monte Carlo method. A Monte Carlo technique generalized to the multi-orbital systems is introduced and examined in detail. The algorithm…
We adapt the Coupled Cluster Method to solid state strongly correlated lattice Hamiltonians extending the Coupled Cluster linear response method to the calculation of electronic spectra and obtaining the space-time Fourier transforms of…
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set,…
Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
We present a quantum-classical hybrid implementation of the Liouvillian recursion method to compute many-body Green's functions using a quantum computer. From an approximate ground state preparation circuit, this algorithm produces the…
This study introduces a systematic approach for analyzing strongly correlated systems by adapting the conventional quantum cluster method to a quantum circuit model. We have developed a more concise formula for calculating the cluster's…
We study the single-band Hubbard model under the action of an external magnetic field using the cumulant Green's functions method (CGFM). The starting point of the method is to diagonalize a cluster containing N correlated sites (seed) and…
The Hubbard model, a cornerstone in the field of condensed matter physics, serves as a fundamental framework for investigating the behavior of strongly correlated electron systems. This paper presents a novel perspective on the model,…
Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We discuss an…
The Hubbard model has often been studied with exact diagonalization (ED). This impurity solver is fundamentally limited by the exponential scaling of the Fock space. To address this problem, we introduce Monte Carlo diagonalization. Using a…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…
An exact analytical diagonalization is used to solve the two dimensional Extended Hubbard Model for system with finite size. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions with interaction…
We present an approach for GW calculations of quasiparticle energies with quasi-quadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method…
By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a…