相关论文: Truncated Unity Parquet Solver

This paper is a continuation of our previous investigations on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, \textbf{63}, no. 6, 786-797, and Ukrainian Math. J., 2013, \textbf{64}, no. 8, 1199-1214. In this…

We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in d dimensions. We use the Truncated Conformal Space Approach (TCSA), a Hamiltonian method which exploits the conformal structure of the…

We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction…

This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…

The parquet equations present a cornerstone of some of the most important diagrammatic many-body approximations and methods currently on the market for strongly correlated materials: from non-local extensions of the dynamical mean-field…

Taking the competition and the mutual screening of various bosonic fluctuations in correlated electron systems into account requires an unbiased approach to the many-body problem. One such approach is the self-consistent solution of the…

In this paper we study the truncated matrix trigonometric moment problem. We obtained a bijective parameterization of all solutions of this moment problem (both in nondegenerate and degenerate cases) via an operator approach. We use…

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently,…

We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call step-truncation methods, are based on performing one time step with a conventional…

A coupled-cluster approach for systems of $N$ bosons in external traps is developed. In the coupled-cluster approach the exact many-body wavefunction is obtained by applying an exponential operator $\exp{T}$ to the ground configuration…

Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number…

Representing the time-evolution operator as a tensor network constitutes a key ingredient in several algorithms for studying quantum lattice systems at finite temperature or in a non-equilibrium setting. For a Hamiltonian composed of…

We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We…

Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator…

We obtain a new multiplicative decomposition of the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem in the case of an odd and even number of moments via new Dyukarev-Stieltjes matrix (DSM) parameters. Explicit…

A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…

In this paper we study the truncated operator trigonometric moment problem. All solutions of the moment problem are described by a Nevanlinna-type parameterization. In the case of moments acting in a separable Hilbert space, the matrices of…

We introduce a new strategy in solving the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed \emph{moment}…

We propose a Forward-Backward Truncated-Newton method (FBTN) for minimizing the sum of two convex functions, one of which smooth. Unlike other proximal Newton methods, our approach does not involve the employment of variable metrics, but is…

We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…