Related papers: Notes on density matrix perturbation theory

We introduce a perturbative approximation to the combined density functional theory and multireference configuration interaction (DFT/MRCI) method. The method, termed DFT/MRCI(2), results from the application of quasi-degenerate…

We define and classify symmetry-protected topological (SPT) phases in mixed states based on the tensor network formulation of the density matrix. In one dimension, we introduce strong injective matrix product density operators (MPDO), which…

We present in full detail a newly developed formalism enabling density functional perturbation theory (DFPT) calculations from a DFT+$U$ ground state. The implementation includes ultrasoft pseudopotentials and is valid for both insulating…

Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…

Many problems in physics, chemistry and other fields are perturbative in nature, i.e. differ only slightly from related problems with known solutions. Prominent among these is the eigenvalue perturbation problem, wherein one seeks the…

Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under…

In large-scale optimization, when either forming or storing Hessian matrices are prohibitively expensive, quasi-Newton methods are often used in lieu of Newton's method because they only require first-order information to approximate the…

We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering of collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. We show that VPT can be cast into a form…

We extend to additional probability measures and scenarios, certain of the recent results of Krattenthaler and Slater (quant-ph/9612043), whose original motivation was to obtain quantum analogs of seminal work on universal data compression…

With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…

We develop a variant of the density matrix renormalization group (DMRG) algorithm for two-dimensional cylinders that uses a real space representation along the cylinder and a momentum space representation in the perpendicular direction. The…

This chapter presents the theory behind the CASPT2 method and its adaptation to a multi-state formalism. The chapter starts with an introduction of the theory of the CASPT2 method - an application of Rayleigh-Schr\"odinger perturbation…

We consider the product of determinantal point processes (DPPs), a point process whose probability mass is proportional to the product of principal minors of multiple matrices, as a natural, promising generalization of DPPs. We study the…

Perturbation theory (PT) calculation of large-scale structure has been used to interpret the observed non-linear statistics of large-scale structure at the quasi-linear regime. In particular, the so-called standard perturbation theory (SPT)…

Multiconfiguration pair-density functional theory (MC-PFDT) has previously been applied successfully to carry out ground-state and excited-state calculations. However, because it includes no interaction between electronic states, MC-PDFT…

We present two efficient and intruder-free methods for treating dynamic correlation on top of general multi-configuration reference wave functions---including such as obtained by the density matrix renormalization group (DMRG) with large…

Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the…

We propose an initialization procedure for the density-matrix renormalization group (DMRG): {\it the recursive sweep method}. In a conventional DMRG calculation, the infinite-algorithm, where two new sites are added to the system at each…

We present a density matrix approach for computing global solutions of Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. Equality of the upper- and…

DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation…