arXiv subjects

Nan Sheng

Publications and source records attributed to Nan Sheng.

At least 19 recordsLinked to original sources

arXiv2026

Full-State and Reduced-Moment Encodings: A Representation-Level View of Equilibrium Quantum Many-Body Theory

Equilibrium quantum many-body methods differ not only in approximation, but in which information they represent explicitly. We formulate this distinction by fixing an equilibrium specification and viewing every representation as an encoder from admissible states to represented variables. The identity encoder gives a full-state representation, whereas a non-injective encoder gives a reduced representation whose value labels a fiber of compatible states. For a specified task, an exact decoder exists on a state class if and only if the task is constant on the encoder fibers within that class. Variational principles, reconstruction correspondences, functionals, kernels, and closures are different realizations of additional structure used to select, restrict, or approximate the task-relevant content of a fiber when the retained variable alone is insufficient. Static moments and imaginary-time correlation functions are unified as restrictions of a complete equilibrium readout functional to different probe families. Within the same principle, quantum embedding can be viewed as consistency or replacement between global and local descriptions through reduced interface encoders and their conjugate fields.

physics.chem-ph↗

arXiv2026

RPA as a Hessian Closure: Effective Functionals and Source-Variable Duality Across DFT, LR-TDDFT, 1RDMFT, and MBPT

We present a variational formulation of the random phase approximation (RPA) that places density functional theory (DFT), linear-response time-dependent density functional theory (LR-TDDFT), one-body reduced density matrix functional theory (1RDMFT), and Green's function many-body perturbation theory (MBPT) into a common source-variable hierarchy. The central claim is that a broad class of RPA constructions can be organized, independently of any one problem-specific formula, diagrammatic resummation, or small-amplitude equation of motion, as closure approximations to the exact Hessian of an effective functional. In this language, exact linear response is governed by the Hessian of the corresponding effective functional, while RPA is obtained by retaining a reference contribution together with an explicit interaction kernel and discarding the irreducible remainder. The hierarchy has two independent enrichments of the density-level description. One may enlarge the static local density to a time-dependent density, giving the dynamical density channel of LR-TDDFT, or enlarge it to an equal-time bilocal one-body reduced density matrix, giving the static bilocal channel of 1RDMFT. The Green's function level combines both enrichments, since the one-particle Green's function is bilocal in both space and time. This picture clarifies the relation between DFT, LR-TDDFT, 1RDMFT, and MBPT through exact forward reductions and source restrictions, while emphasizing that the corresponding RPA closures need not commute under projection. The hierarchy also distinguishes the local branch-wise Legendre geometry common to all four levels from the stronger global convex duality that may emerge only in source sectors possessing additional positivity and global regularity.

physics.chem-ph↗

arXiv2026

ERNIE-Image Technical Report

We introduce ERNIE-Image, an open-source text-to-image generation model built upon an 8B single-stream DiT architecture. ERNIE-Image aims to bridge the gap between current open-source models and leading closed-source systems through more effective mining of large-scale pre-training data and improved supervision quality throughout training. During pre-training, we adopt a bottom-up data construction pipeline that combines fine-grained image categorization, rich caption annotation, aesthetic assessment, and hierarchical sampling. This strategy reduces data noise while preserving long-tail concepts and detailed real-world knowledge, providing a stronger foundation for complex generation tasks. In the post-training stage, we use a top-down data construction pipeline for high-demand scenarios, diversify prompt annotations to better match real user inputs, and apply a stabilized DPO strategy to align the model with human aesthetic preferences. We further train ERNIE-Image-Turbo for efficient 8-NFE generation and propose MT-DMD to mitigate capability drift during distillation. To make the model easier to use in practical scenarios, we equip it with a lightweight Prompt Enhancer that expands concise user intents into structured visual descriptions. In addition, we develop ERNIE-Image-Aes, an industrial-grade aesthetic model, together with ERNIE-Image-Aes-1K, a human-annotated benchmark for realistic aesthetic evaluation. Extensive qualitative and quantitative experiments show that ERNIE-Image achieves leading performance among open-source models and approaches top-tier commercial models in instruction following, text rendering, and aesthetic quality. We release the trained models and aesthetic resources to facilitate further academic research and technical progress in the AIGC community.

cs.CV↗

arXiv2026

Agentic Discovery of Exchange-Correlation Density Functionals

The development of accurate exchange-correlation (XC) functionals remains a longstanding challenge in density functional theory (DFT). The vast majority of XC functionals have been hand designed by human researchers combining physical insight, exact constraints, and empirical fitting. Recent advances in large language models enable a systematic, automated alternative to this human-driven design loop. This report presents an agentic search system in which an LLM proposes structured functional-form changes guided by evolutionary history. The system attempts to improve functional performance through an iterative plan-execute-summarize loop, where improvements are measurable by optimizing functional parameters against a standard thermochemistry dataset, then evaluating performance on a held-out subset. The strongest discovered functional, SAFS26-a (Seed Agentic Functional Search 2026), improves upon the gold-standard {\omega}B97M-V baseline by ~9%. These results also surface a cautionary lesson for AI-assisted science: models powerful enough to discover genuine improvements are equally capable of exploiting unphysical shortcuts to game the benchmark; domain expertise translated into explicitly enforced constraints remains essential to keeping results scientifically grounded.

cs.AI↗

arXiv2026

A density-functional perspective on force fields

Force fields are usually formulated directly in nuclear configuration space, whereas density functional theory is naturally formulated in terms of external potentials, densities, and variational duality. We show that exact force fields are variationally induced by DFT: the Born-Oppenheimer potential-energy surface is the pullback of the external-potential energy functional along the map from nuclear configurations to Coulomb potentials. In the Lieb formulation of density functional theory, the density is the first functional derivative of the energy with respect to the external potential, while the density-density response function is the second. Pulling these derivative objects back to nuclear configuration space yields the force and the nuclear Hessian, together with explicit terms induced by the nuclear-generated potential and the nuclear-nuclear repulsion. The resulting picture places force fields, density functional theory, and response theory within a single derivative hierarchy. The purpose of the present work is conceptual rather than algorithmic.

physics.chem-ph↗

arXiv2026

Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn-Sham theory

Exact density-functional theory is recast here as two parallel exact ensemble variational hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in exact noninteracting ensemble theory. In optimization terms, $N$-representability is primal feasibility, Legendre-Fenchel duality equates the primal and dual values, $v$-representability is dual attainment, and the Hohenberg-Kohn theorem gives uniqueness, modulo constants, of an attained local potential. The Kohn-Sham construction couples the interacting density-space optimality condition to a compatible noninteracting dual realization on their common $N$-representable density domain. State-class restrictions yield the Levy-Lieb and single-determinant branches, while fractional particle number and fractional occupations lead naturally to piecewise linearity, one-sided chemical potentials, Janak-type relations, and the derivative discontinuity. This organization locates the exactness of Kohn-Sham theory in the preservation of the interacting density-space optimization together with its compatible noninteracting realization, without implying a general many-body spectral interpretation of Kohn-Sham eigenvalues.

physics.chem-ph↗

arXiv2026

A unified variational framework for the inverse Kohn-Sham problem

The inverse Kohn-Sham (KS) problem seeks a local effective potential whose noninteracting ground state reproduces a prescribed electron density. Although many inversion formulations and schemes have been developed, they are often formulated in disparate languages, including reduced variational optimization, penalty regularization, response-based iteration, and PDE-constrained optimization. In this work, we develop a unified framework for inverse KS theory in two steps. First, we identify the fixed-density noninteracting constrained search and its density-potential duality as the natural variational anchor of the inverse KS problem. In this setting, the KS potential appears as the variational dual object associated with density reproduction, reducing to the familiar multiplier picture in regular regimes. Second, building on this anchor, we classify major inversion formulations according to how the KS state equations and density-reproduction condition are treated within the optimization architecture, with orbital orthonormality retained as an additional structural constraint. Within this framework, the Wu-Yang formulation appears as a potential-space reduced multiplier formulation, the Zhao-Morrison-Parr construction as a quadratic-penalty relaxation, and PDE-constrained approaches as explicit state-constraint formulations at the orbital level. Rather than comparing inversion formulations primarily at the level of implemented algorithms, the present work develops an optimization-theoretic formulation map. This viewpoint identifies where additive-constant ambiguity, asymptotic normalization, nonsmooth variational structure, metric choice, and weak-gap instability enter different inversion architectures, and it makes explicit how major inversion approaches are connected and where algorithmic design choices arise.

physics.chem-ph↗

arXiv2025

Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors

The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing a particle-based high-dimensional parametric density estimation subroutine, and the input to the subroutine is Gibbs samples generated by leveraging advanced sampling techniques. Specifically, to generate Gibbs samples, we employ ensemble-based annealed importance sampling, a population-based approach for sampling multimodal distributions. These samples are then processed using functional hierarchical tensor sketching, a tensor-network-based density estimation method for high-dimensional distributions, to obtain the numerical representation of the Gibbs distribution. We successfully apply the proposed approach to complex Ginzburg-Landau models with hundreds of variables. In particular, we show that the approach proposed is successful at addressing the metastability issue under difficult numerical cases.

math.NA↗

arXiv2024

Solving high-dimensional Hamilton-Jacobi-Bellman equation with functional hierarchical tensor

This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a particle under Brownian motion. In particular, the existence of diffusion presents a new challenge to conventional tensor network methods for deterministic optimal control. To overcome the difficulty, we use a general regression-based formulation where the loss term is the Bellman consistency error combined with a Sobolev-type penalization term. We propose two novel sketching-based subroutines for obtaining the tensor-network approximation to the action-value functions and the value functions, which greatly accelerate the convergence for the subsequent regression phase. We apply the proposed approach successfully to two challenging control problems with Ginzburg-Landau potential in 1D and 2D with 64 variables.

math.NA↗

arXiv2023

Low rank Green's function representations applied to dynamical mean-field theory

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low-rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular, show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of Sr$_2$RuO$_4$ at temperature $50$K using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only $36$ nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

cond-mat.str-el↗

arXiv2022

Quantum simulations of Fermionic Hamiltonians with efficient encoding and ansatz schemes

We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum eigensolvers (VQE). We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubit-coupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamond and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time.

quant-ph↗

arXiv2022

Partial Residuated Implications Derived from Partial Triangular Norms and Partial Residuated Lattices

In this paper, we reveal some relations between fuzzy logic and quantum logic, and mainly study the partial residuated implications (PRIs) derived from partial triangular norms (partial t-norms) and partial residuated lattices (PRLs), and expand some results in the article "material implication in lattice effect algebra". Firstly, according to the concept of partial triangular norms given by Borzooei, we introduce the connection between lattice effect algebra and partial t-norms, and prove that partial operations in any commutative quasiresiduated lattice are partial t-norms. Secondly, we give the general form of partial residuated implications and the concept of partial fuzzy implications (PFIs), and the condition that partial residuated implication is a fuzzy implication is given. We also prove that each partial residuated implication is a partial fuzzy implication. Thirdly, we propose the partial residuated lattice and study their basic properties, to discuss the corresponding relationship between PRLs and lattice effect algebras (LEAs), to further reveal the relationship between LEAs and residuated partial algebras. In addition, like the definition of partial t-norms, we also propose the concepts of partial triangular conorms (partial t-conorms) and corresponding partial co-residuated lattices (PcRLs). Finally, based on partial residuated lattices, we give the definition of well partial residuated lattices (wPRLs), study the filter of well partial residuated lattices, and then construct quotient structure of partial residuated lattices.

cs.LO↗

arXiv2022

Quantum Embedding Theories to Simulate Condensed Systems on Quantum Computers

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate scale quantum computers using embedding theories, and we give examples for a specific class of materials, i.e., spin defects in solids. These are promising systems to build future quantum technologies, e.g., computers, sensors and devices for quantum communications. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

quant-ph↗

arXiv2022

Green's function formulation of quantum defect embedding theory

We present a Green's function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the $G_0 W_0$ approximation. We then show the robustness of our methodology by applying the theory with the newly derived scheme to several defects in diamond. Additionally, we discuss a strategy to obtain converged results as a function of the size and composition of the active space. Our results show that QDET is a promising approach to investigate strongly correlated states of defects in solids.

quant-ph↗

arXiv2021

Quantum Embedding Theory for Strongly-correlated States in Materials

Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We present a detailed derivation of a quantum embedding theory recently introduced, which is based on the definition of effective Hamiltonians. The effect of the environment on a chosen active space is accounted for through screened Coulomb interactions evaluated using density functional theory. Importantly, the random phase approximation is not required and the evaluation of virtual electronic orbitals is circumvented with algorithms previously developed in the context of calculations based on many-body perturbation theory. In addition, we generalize the quantum embedding theory to active spaces composed of orbitals that are not eigenstates of Kohn-Sham Hamiltonians. Finally, we report results for spin defects in semiconductors.

cond-mat.mtrl-sci↗

arXiv2020

First-principles Studies of Strongly Correlated States in Defect Spin Qubits in Diamond

Using a recently developed quantum embedding theory, we present first principles calculations of strongly correlated states of spin defects in diamond. Within this theory, effective Hamiltonians are constructed, which can be solved by classical and quantum computers; the latter promise a much more favorable scaling as a function of system size than the former. In particular, we report a study of the neutral group-IV vacancy complexes in diamond, and we discuss their strongly-correlated spin-singlet and spin-triplet excited states. Our results provide valuable predictions for experiments aimed at optical manipulation of these defects for quantum information technology applications.

cond-mat.mtrl-sci↗

arXiv2016

Asymmetric Nanoparticle May Go Active at Room Temperature

Using molecular dynamics simulations, we show that an asymmetrically shaped nanoparticle in dilute solution possesses a spontaneously curved trajectory within finite time interval, instead of the generally expected random walk. This unexpected dynamic behavior has a similarity to that of active matters, such as swimming bacteria, cells or even fishes, but is of a different physical origin. The key to the curved trajectory lies in the non-zero resultant force originated from the imbalance of the collision forces acted by surrounding solvent molecules on the shaped nanoparticle during its orientation regulation. Theoretical formulae based on the microscopic observation have been derived to describe this non-zero force and the resulted motion of the nanoparticle.

cond-mat.soft↗

arXiv2016

Spontaneous Directional Motion of Shaped Nanoparticle

In nanoscale space and pico- to nanoseconds enormous physical, chemical and biological processes take place, while the motions of involved particles/molecules under thermal fluctuations are usually analyzed using the conventional theory of diffusive Brownian motion based on both sufficiently long time averaging and assumptions of spherical particle shapes. Here, using molecular dynamics simulations, we show that asymmetrically shaped nanoparticles in dilute solutions possess spontaneous directional motion of the center of mass within a finite time interval. The driving force for this unexpected directional motion lies in the imbalance of the interactions experienced by their constituent atoms during the orientation regulation at timescales before the onset of diffusive Brownian motion. Theoretical formulae have been derived to describe the mean displacement and the variance of this directional motion. Our study potentially takes an important step towards establishing a complete theoretical framework for describing the motions of variously-shaped particles in solutions over all timescales from ballistic to diffusive regime.

cond-mat.soft↗