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The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the…

The symmetrized Density-Matrix-Renormalization-Group (DMRG) method is used to study linear and nonlinear optical properties of Free base porphine and metallo-porphine. Long-range interacting model, namely, Pariser-Parr-Pople (PPP) model is…

Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their…

Single-particle resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory. Taking the neutron resonant…

Continuous Matrix Product States (cMPS) are powerful variational ansatz states for ground states of continuous quantum field theories in (1+1) dimension. In this paper we introduce a novel parametrization of the cMPS wave function based on…

This paper extends the inverse substructuring (IS) approach to the state-space domain and presents a novel state-space substructuring (SSS) technique that embeds the dynamics of connecting elements (CEs) in the Lagrange Multiplier…

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ~20 electrons in ~20 orbitals…

Matchgates and Clifford circuits are two types of quantum circuits which can be efficiently simulated classically, though the underlying reasons are quite different. Matchgates are essentially the single particle basis transformations in…

The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two…

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of rapidly performing the infinite system density matrix renormalization group (DMRG)…

We present a family of \textit{Gaussian Mixture Approximation} (GMA) samplers for sampling unnormalised target densities, encompassing \textit{weights-only GMA} (W-GMA), \textit{Laplace Mixture Approximation} (LMA),…

We employ Statistical Field Theory techniques for coarse-graining the steady-state properties of Active Ornstein-Uhlenbeck particles. The computation is carried on in the framework of the Unified Colored Noise approximation that allows an…

We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al (J. Chem. Theor.Comput. 9, 4462 (2013)). We introduce a DMRG wavefunction maximum overlap…

The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important…

The renormalization of a system of coupled scalars fields is analyzed. By introducing a momentum dependent mixing angle we diagonalize the inverse propagator matrix at any momentum $p^2$. The zeros of the inverse propagator matrix, \ie, the…

We present a comprehensive convergence analysis for Self-Consistent Field (SCF) iteration to solve a class of nonlinear eigenvalue problems with eigenvector-dependency (NEPv). Using a tangent-angle matrix as an intermediate measure for…

Density matrix embedding theory (DMET) is a fully quantum-mechanical embedding method which shows great promise as a method of defeating the inherent exponential cost scaling of multiconfigurational wave function-based calculations by…

We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix…

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…

A deterministic-stochastic coupling scheme is developed for simulating rarefied gas flows, where the key process is the alternative solving of the macroscopic synthetic equations [Su et al., J. Comput. Phys., 407 (2020) 109245] and the…