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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…
In this paper, we first derive a theoretical basis for spherical conformal parameterizations between a simply connected closed surface $\mathcal{S}$ and a unit sphere $\mathbb{S}^2$ by minimizing the Dirichlet energy on…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
We investigate the efficient combination of the canonical polyadic decomposition (CPD) and tensor hyper-contraction (THC) approaches. We first present a novel low-cost CPD solver which leverages a precomputed THC factorization of an…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4…
We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of…
Low-scaling electron correlation theory based on the pair natural orbital approximation, PNO-CCSD(T), has become a powerful computational tool. Motivated by the recent discovery of large errors for organometallic molecules, we assess the…
Real-time coupled cluster (CC) methods have several advantages over their frequency-domain counterparts, namely, response and equation of motion CC theories. Broadband spectra, strong fields, and pulse manipulation allow for the simulation…
The many-body perturbation theory within the $GW$ approximation is a widely used method for describing the electronic band structures in real materials. Its application to large-scale systems is, however, impeded by its high computational…
We present two approaches for enhancing the accuracy of second order finite difference approximations of two-dimensional semilinear parabolic systems. These are the fourth order compact difference scheme and the fourth order scheme based on…
We derive and motivate a Laplacian-level, orbital-free meta-generalized-gradient approximation (LL-MGGA) for the exchange-correlation energy, targeting accurate ground-state properties of $sp$ and $sd$ metallic condensed matter, in which…
Several methods are available to compute the anharmonicity in semi-rigid molecules. However, such methods are not routinely employed yet because of their large computational cost, especially for large molecules. The potential energy surface…
Quantum computation offers significant potential for accelerating the simulation of molecules and materials through algorithms such as quantum phase estimation (QPE). However, the expected speedup in ground-state energy estimation depends…
We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in…
The out-of-time-order correlator (OTOC) of simple harmonic oscillator with extra anharmonic (quartic) interaction are calculated by the second quantization method. We obtain the analytic formulas of spectrum, Fock space states and matrix…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
First principles calculations based on density functional theory are having an incerasing impact on our understanding of molecule-surface interactions. For example, calculations of the multi-dimensional potential energy surface have…
The gravitational wave sky is starting to become very crowded, with the fourth science run (O4) at LIGO expected to detect $\mathcal{O}(100)$ compact object coalescence signals. Data analysis issues start to arise as we look further…
We consider the massively parallel computation (MPC) model, which is a theoretical abstraction of large-scale parallel processing models such as MapReduce. In this model, assuming the widely believed 1-vs-2-cycles conjecture, solving many…