arXiv subjects

Ke Liao

Publications and source records attributed to Ke Liao.

15 recordsLinked to original sources

arXiv2026

Interpolative Separable Density-Fitting for Transcorrelated Hamiltonians

The transcorrelated (TC) method dramatically accelerates the convergence of correlated calculations toward the complete-basis-set (CBS) limit by folding a Jastrow correlator into the Hamiltonian via a similarity transformation, incorporating the electron--electron cusp into the effective interaction. We make the TC framework practical for large systems and flexible, multi-center correlators by compressing the grid-evaluated TC integrals with the interpolative separable density-fitting (ISDF) approximation, combined with the effective two-body (xTC) treatment of the three-body operator. This low-rank representation reduces storage and integration costs by orders of magnitude, and a multi-GPU implementation with automatic differentiation of the correlator makes the construction routine for large basis sets. We demonstrate the resulting ISDF-xTC-CCSD method on the linear hydrogen chain, reaching the joint thermodynamic and CBS limits with basis sets up to cc-pV5Z in agreement with state-of-the-art many-body references to within about 1~mHa/atom, and on the benzene ground-state energy with up to 1200 orbitals (cc-pCV5Z), where the method attains state-of-the-art accuracy at the coupled cluster singles and doubles level and its CBS extrapolation is markedly more robust than that of conventional coupled-cluster methods.

physics.chem-ph↗

arXiv2024

Energy-filtered excited states and real-time dynamics served in a contour integral

It is observed that the Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain. This forms the theoretical foundation for applying various operators in the form of a contour integral to a state, while filtering away eigen-components that are not included by the contour. As a special case, the identity operator in the integral form--the Riesz projector--is used to design an algorithm for finding a given number of eigen-pairs whose energies are close to a specified value in the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) framework, with applications to calculate core excited states of molecules which is relevant for the X-ray absorption spectroscopy (XAS). As a generalization, I showcase a novel real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF form of the exponential time-evolution operator, which admits extremely large time steps while preserving accurate spectral information.

physics.chem-ph↗

arXiv2024

What Can Quantum Information Theory Offer to Quantum Chemistry?

It is the ultimate goal of this work to foster synergy between quantum chemistry and the flourishing field of quantum information theory. For this, we first translate quantum information concepts such as entanglement and correlation into the context of quantum chemical systems. In particular, we establish two conceptually distinct perspectives on `electron correlation' leading to a notion of orbital and particle correlation. We then demonstrate that particle correlation equals total orbital correlation minimized over all orbital bases. Accordingly, particle correlation resembles the minimal, thus intrinsic, complexity of many-electron wave functions while orbital correlation quantifies their complexity relative to a basis. We illustrate these concepts of intrinsic and extrinsic correlation complexity in molecular systems, which also manifests the crucial link between the two correlation pictures. Our results provide theoretical justification for the long-favored natural orbitals for simplifying electronic structures, and open new pathways for developing more efficient approaches towards the electron correlation problem.

quant-ph↗

arXiv2024

Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality

The simultaneous treatment of static and dynamical correlations in strongly-correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the representational complexity of the many-body wavefunction is a formidable and longstanding problem. As a substantial contribution towards its solution, we show that the total orbital correlation actually reveals and quantifies the intrinsic complexity of the wavefunction,once it is minimized via orbital rotations. To demonstrate the power of this concept in practice, an iterative scheme is proposed to optimize the orbitals by minimizing the total orbital correlation calculated by the tailored coupled cluster singles and doubles (TCCSD) ansatz. The optimized orbitals enable the limited TCCSD ansatz to capture more non-trivial information of the many-body wavefunction, indicated by the improved wavefunction and energy. An initial application of this scheme shows great improvement of TCCSD in predicting the singlet ground state potential energy curves of the strongly correlated C$_{\rm 2}$ and Cr$_{\rm 2}$ molecule.

quant-ph↗

arXiv2023

Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond

Block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency, and to support integration with external numerical packages. Here we explain the design principles and currently supported features and present numerical examples in a range of applications.

physics.chem-ph↗

arXiv2023

Tunable magnetism and electron correlation in Titanium-based Kagome metals RETi3Bi4 (RE = Yb, Pr, and Nd) by rare-earth engineering

Rare-earth engineering is an effective way to introduce and tune the magnetism in topological Kagome magnets, which has been acting as a fertile platform to investigate the quantum interactions between geometry, topology, spin, and correlation. Here we report the structure and properties of three newly discovered Titanium-based Kagome metals RETi3Bi4 (RE = Yb, Pr, and Nd) with various magnetic states. They crystalize in the orthogonal space group Fmmm (No.69), where slightly distorted Ti Kagome lattice, RE triangular lattice, Bi honeycomb and triangular lattices stack along the a axis. By changing the rare earth atoms on RE zag-zig chains, the magnetism can be tuned from nonmagnetic YbTi3Bi4 to short-range ordered PrTi3Bi4 (Tanomaly ~ 8.2 K), and finally to ferromagnetic NdTi3Bi4 (Tc ~ 8.5 K). The measurements of resistivity and specific heat capacity demonstrate an evolution of electron correlation and density of states near the Fermi level with different rare earth atoms. In-situ resistance measurements of NdTi3Bi4 under high pressure further reveal a potential relationship between the electron correlation and ferromagnetic ordering temperature. These results highlight RETi3Bi4 as another family of topological Kagome magnets to explore nontrivial band topology and exotic phases in Kagome materials.

cond-mat.str-el↗

arXiv2023

Structure, physical properties, and magnetically tunable topological phases in topological semimetal EuCuBi

A single material achieving multiple topological phases can provide potential application for topological spintronics, whereas the candidate materials are very limited. Here, we report the structure, physical properties, and possible emergence of multiple topological phases in the newly discovered, air-stable EuCuBi single crystal. EuCuBi crystallizes in a hexagonal space group P63/mmc (No. 194) in ZrBeSi-type structure with an antiferromagnetic (AFM) ground state below TN = 11.2 K. There is a competition between AFM and ferromagnetic (FM) interactions below TN revealed by electrical resistivity and magnetic susceptibility measurements. With the increasing magnetic field, EuCuBi evolves from the AFM ground state with a small amount of FM component, going through two possible metamagnetic phases, finally reaches the field-induced FM phase. Based on the first-principles calculations, we demonstrate that the Dirac, Weyl, and possible mirror Chern insulator can be achieved in EuCuBi by tuning the temperature and applying magnetic field, making EuCuBi a promising candidate for exploring multiple topological phases.

cond-mat.mtrl-sci↗

arXiv2023

Ab Initio Transcorrelated Method enabling accurate Quantum Chemistry on near-term Quantum Hardware

Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields, including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and limited connectivity) hamper the straightforward implementation of most quantum algorithms and call for more noise-resilient solutions. In quantum chemistry, the limited number of available qubits and gate operations is particularly restrictive since, for each molecular orbital, one needs, in general, two qubits. In this study, we propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach, which transfers -- without any approximation -- correlation from the wavefunction directly into the Hamiltonian, thus reducing the number of resources needed to achieve accurate results with noisy, near-term quantum devices. In particular, we show that the exact transcorrelated approach not only allows for more shallow circuits but also improves the convergence towards the so-called basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, therefore, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using just 4 and 6 qubits, respectively. Conventional methods require at least ten times more qubits for the same accuracy.

quant-ph↗

arXiv2023

Physical properties, electronic structure, and strain-tuned monolayer of the weak topological insulator RbTi3Bi5 with Kagome lattice

Kagome metals AV3Sb5 (A = K, Rb, and Cs) with a V-Kagome lattice acting as a fertile platform to investigate geometric frustration, electron correlation, superconductivity, and nontrivial band topology, have attracted tremendous attention. Here we reported the structure and properties of ATi3Bi5 (A = Rb, Cs) family with a Ti-Kagome lattice, specifically focusing on the electronic structure and nontrivial band topology of RbTi3Bi5. ATi3Bi5 (A = Rb, Cs) is found to be non-superconducting metal with strong quasi-two-dimensional feature, moderate electron correlation, and small Pauli paramagnetism. Based on first principles calculations, RbTi3Bi5 is determined to be a weak topological insulator with gapless surface states along (100) plane, and the electronic band structure along (001) plane is in great agreement with experimentally observed one. In particular, the electronic properties of the RbTi3Bi5 monolayer can be efficiently tuned by a biaxial strain according to calculation, with its lower saddle points coming from Kagome lattice approaching the Fermi level. These results highlight ATi3Bi5 (A = Rb, Cs) with Ti-Kagome lattice is a new Kagome metal to explore nontrivial band topology and exotic phases.

cond-mat.supr-con↗

arXiv2022

Does Deep Learning REALLY Outperform Non-deep Machine Learning for Clinical Prediction on Physiological Time Series?

Machine learning has been widely used in healthcare applications to approximate complex models, for clinical diagnosis, prognosis, and treatment. As deep learning has the outstanding ability to extract information from time series, its true capabilities on sparse, irregularly sampled, multivariate, and imbalanced physiological data are not yet fully explored. In this paper, we systematically examine the performance of machine learning models for the clinical prediction task based on the EHR, especially physiological time series. We choose Physionet 2019 challenge public dataset to predict Sepsis outcomes in ICU units. Ten baseline machine learning models are compared, including 3 deep learning methods and 7 non-deep learning methods, commonly used in the clinical prediction domain. Nine evaluation metrics with specific clinical implications are used to assess the performance of models. Besides, we sub-sample training dataset sizes and use learning curve fit to investigate the impact of the training dataset size on the performance of the machine learning models. We also propose the general pre-processing method for the physiology time-series data and use Dice Loss to deal with the dataset imbalanced problem. The results show that deep learning indeed outperforms non-deep learning, but with certain conditions: firstly, evaluating with some particular evaluation metrics (AUROC, AUPRC, Sensitivity, and FNR), but not others; secondly, the training dataset size is large enough (with an estimation of a magnitude of thousands).

cs.LG↗

arXiv2022

Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in \emph{ab initio} Systems

We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians, and show applications in \emph{ab initio} molecular systems. Transcorrelation (TC) accelerates the basis set convergence rate by including known physics (such as, but not limited to, the electron-electron cusp) in the Jastrow factor used for the similarity transformation. It also improves the accuracy of approximate methods such as coupled cluster singles and doubles (CCSD) as shown by some recent studies. However, the non-Hermiticity of the TC Hamiltonians poses challenges for variational methods like DMRG. Imaginary-time evolution on the matrix product state (MPS) in the DMRG framework has been proposed to circumvent this problem; but this is currently limited to treating the ground state, and has lower efficiency than the time-independent DMRG (TI-DMRG), due to the need to eliminate Trotter errors. In this work, we show that with minimal changes to the existing TI-DMRG algorithm, namely replacing the original Davidson solver with the general Davidson solver to solve the non-Hermitian effective Hamiltonians at each site for a few low-lying right eigenstates, and following the rest of the original DMRG recipe, one can find the ground and excited states with improved efficiency compared to the original DMRG when extrapolating to the infinite bond dimension limit in the same basis set. Accelerated basis set convergence rate is also observed, as expected, within the TC framework.

physics.chem-ph↗

arXiv2021

Towards efficient and accurate \emph{ab initio} solutions to periodic systems via transcorrelation and coupled cluster theory

We propose a streamlined combination scheme of the transcorrelation (TC) and coupled cluster (CC) theory, which not only increases the convergence rate with respect to the basis set, but also extends the applicability of the lowest order CC approximations to strongly correlated regimes in the three dimensional uniform electron gas (3D UEG). With the correct physical insights built into the correlator used in TC, highly accurate ground state energies with errors $\leq 0.001 $ a.u./electron relative to the state-of-the-art quantum Monte Carlo results can be obtained across a wide range of densities. The greatly improved efficiency and accuracy of our methods hold great promise for strongly correlated solids where many other methods fail.

cond-mat.str-el↗

arXiv2020

Structural and electronic properties of solid molecular hydrogen from many-electron theories

We study the structural and electronic properties of phase III of solid hydrogen using accurate many-electron theories and compare to state-of-the-art experimental findings. The atomic structures of phase III modelled by C2/c-24 crystals are fully optimized on the level of second-order perturbation theory, demonstrating that previously employed structures optimized on the level of approximate density functionals exhibit errors in the H$_2$ bond lengths that cause significant discrepancies in the computed quasi particle band gaps and vibrational frequencies compared to experiment. Using the newly optimized atomic structures, we study the band gap closure and change in vibrational frequencies as a function of pressure. Our findings are in good agreement with recent experimental observations and may prove useful in resolving long-standing discrepancies between experimental estimates of metallization pressures possibly caused by disagreeing pressure calibrations.

cond-mat.mtrl-sci↗

arXiv2020

A comparative study using state-of-the-art electronic structure theories on solid hydrogen phases under high pressures

Identifying the atomic structure and properties of solid hydrogen under high pressures is a long-standing problem of high-pressure physics with far-reaching significance in planetary and materials science. Determining the pressure-temperature phase diagram of hydrogen is challenging for experiment and theory due to the extreme conditions and the required accuracy in the quantum mechanical treatment of the constituent electrons and nuclei, respectively. Here, we demonstrate explicitly that coupled cluster theory can serve as a computationally efficient theoretical tool to predict solid hydrogen phases with high accuracy. We present a first principles study of solid hydrogen phases at pressures ranging from 100 to 450 GPa. The computed static lattice enthalpies are compared to state-of-the-art diffusion Monte Carlo results and density functional theory calculations. Our coupled cluster theory results for the most stable phases including C2/c-24 and P21/c-24 are in good agreement with those obtained using diffusion Monte Carlo, with the exception of Cmca-4, which is predicted to be significantly less stable. We discuss the scope of the employed methods and how they can contribute as efficient and complementary theoretical tools to solve the long-standing puzzle of understanding solid hydrogen phases at high pressures.

cond-mat.mtrl-sci↗

arXiv2020

Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit

Modern electronic structure theories can predict and simulate a wealth of phenomena in surface science and solid-state physics. In order to allow for a direct comparison with experiment, such ab initio predictions have to be made in the thermodynamic limit, substantially increasing the computational cost of many-electron wave-function theories. Here, we present a method that achieves thermodynamic limit results for solids and surfaces using the "gold standard" coupled cluster ansatz of quantum chemistry with unprecedented efficiency. We study the energy difference between carbon diamond and graphite crystals, adsorption energies of water on h-BN, as well as the cohesive energy of the Ne solid, demonstrating the increased efficiency and accuracy of coupled cluster theory for solids and surfaces.

cond-mat.mtrl-sci↗