Related papers: Variational solution of congruent transformed Hami…
We present an extension of the spin-adapted configuration-interaction method for the computation of four electrons in a quasi two-dimensional quantum dot. By a group-theoretical decomposition of the basis set and working with relative and…
A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic…
The effective spin Hamiltonian is constructed in the framework of the almost half-filled Hubbard model on the Cayley tree by means of functional integral technique with the use of static approximation. The system in the ground state appears…
We present the reaction-coordinate polaron-transform (RCPT) framework for generating effective Hamiltonian models to treat nonequilibrium open quantum systems at strong coupling with their surroundings. Our approach, which is based on two…
We consider a nonrelativistic electron interacting with a classical magnetic field pointing along the $x_{3}$-axis and with a quantized electromagnetic field. When the interaction between the electron and photons is turned off, the…
This paper is concerned with variational methods for nonlinear open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. The latter are driven by quantum Wiener processes of the…
Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
Perhaps the simplest first-principles approach to electronic structure is to fit the charge distribution of each orbital pair and use those fits wherever they appear in the entire electron-electron (EE) interaction energy. The charge…
Preparing low energy states is a central challenge in quantum computing and quantum complexity theory. Several known approaches to prepare low energy states often get stuck in suboptimal states, such as high energy eigenstates (or low…
We develop a biorthogonal linear-scaling algorithm for a transcorrelated method based on the localized nature of transformed orbitals. The transcorrelated method, which employs a similarity-transformed Hamiltonian referred to as a…
The limits of direct unitary transformation of many-fermion Hamiltonians are explored. Practical application of such transformations requires that effective many-body interactions be discarded over the course of a calculation. The…
We present a configuration interaction (CI) framework which serves quantitative and conceptual purposes for charge delocalization and electron transfer processes in molecular systems. The electronic Hamiltonian is expressed in a basis of…
Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme…
Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy…
We reanalyze the Hubbard-I approximation by showing that it is equivalent to an effective Hamiltonian describing Fermionic charge fluctuations, which can be solved by Bogoliubov transformation. As the most important correction in the limit…
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…