Related papers: Exact diagonalization: the Bose-Hubbard model as a…
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…
In this study we present an optimization method based on the quantum Monte Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich transformation, employed to decompose the interactions in terms of auxiliary fields,…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using…
In this article the extended Bose-Hubbard model describing ultra-cold atoms confined in a shallow, one-dimensional optical lattice is introduced and studied by the exact diagonalization approach. All parameters of the model are related to…
This paper lays the groundwork for the theory of categorical diagonalization. Given a diagonalizable operator, tools in linear algebra (such as Lagrange interpolation) allow one to construct a collection of idempotents which project to each…
We investigate the quantum dynamics of repulsively bound atom pairs in an optical lattice described by the periodic Bose-Hubbard model both analytically and numerically. In the strongly repulsive limit, we analytically study the dynamical…
In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with sufficiently small backward errors, the magnitude of the resulting…
The Hartree-Fock based diagonalization is a computational method for the investigation of the low-energy properties of correlated electrons in disordered solids. The method is related to the quantum-chemical configuration interaction…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to…
We show how some Hamiltonians may be approximated using rotating wave approximation methods. In order to achieve this we use the algebra of boson ladder operators, and transformation formulas between normal and symmetric ordering of the…
I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric…
Diagonalizing a Hamiltonian, which is essential for simulating its long-time dynamics, is a key primitive in quantum computing and has been proven to yield a quantum advantage for several specific families of Hamiltonians. Yet, despite its…
We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well…
e formulate a method for studying the quantum field dynamics of ultracold Bose gases confined within optical lattice potentials, within the lowest Bloch-band Bose-Hubbard model. Our formalism extends the two-sites results of Phys. Rev.…
Using a similarity Hamiltonian renormalization procedure, we determine an effective spin-1/2 representation of the Bose-Hubbard model at half-integer filling and at a finite on-site interaction energy U. By means of bosonization, we are…
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…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
Within the framework of exact diagonalization (ED), we compute the ground state of Anderson impurity problem using the variational approach based on the configuration interaction (CI) expansion. We demonstrate that an accurate ground state…