Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions

Abraham, Vibin; Mayhall, Nicholas J.

doi:10.1021/acs.jctc.2c00589

Cited by 8 publications

(7 citation statements)

References 87 publications

(139 reference statements)

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“…Moreover, finally, for large imaginary times, this expression will approach the solution of a two-body Schrödinger equation (weighted by the corresponding energy eigenvalue), resulting in a many-body density matrix equivalent to a Jastrow-type wave function. These wave functions are well-known to accurately capture most ground state short-range correlations in systems that exhibit collective phenomena [30,33,34,58,59]. For systems composed of helium atoms, as stated by Leggett [60], the Jastrow function ansatz is the archetypal form of a variational ground state wave function.…”

Section: Pair Product Approximationmentioning

confidence: 99%

Properties of fermionic systems with the path-integral ground state method

et al. 2023

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We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure ^44He systems demonstrate most of the features of the method. Complementarily, for pure ^33He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate ^33He-^44He mixtures, demonstrating the method’s robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature T = 0T=0 without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the ^33He kinetic energy in the mixture.

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Section: Pair Product Approximationmentioning

confidence: 99%

Properties of fermionic systems with the path-integral ground state method

et al. 2023

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“…When those correlations are strong, however, the HF treatment is inadequate. Cluster mean-field (cMF − ) theory generalizes this basic idea but provides a more nuanced and flexible framework. It also uses a wave function which is correct for non-interacting constituents, but where in HF these constituents are the individual electrons, cMF uses multielectronic fragments.…”

Section: Introductionmentioning

confidence: 99%

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

Papastathopoulos-Katsaros,

Henderson,

Scuseria

2024

J. Chem. Theory Comput.

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We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field states and apply it to describe the ground state of strongly correlated spin systems. In cluster mean-field theory, the ground state wave function is expressed as a factorized tensor product of optimized cluster states. While our prior work concentrated on a single cMF tiling, this study removes that constraint by combining different tilings of cMF states. Selection criteria, including translational symmetry and spatial proximity, guide this process. We present benchmark calculations for the one-and two-dimensional J 1 − J 2 and XXZ Heisenberg models. Our findings highlight two key aspects. First, the method offers a semiquantitative description of the 0.4 ≲ J 2 /J 1 ≲ 0.6 regime of the J 1 − J 2 model�a particularly challenging regime for existing methods. Second, our results demonstrate the capability of our method to provide qualitative descriptions for all the models and regimes considered, establishing it as a valuable reference. However, the inclusion of additional (weak) correlations is necessary for quantitative agreement, and we explore methods to incorporate these extra correlations.

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“…In the rank-1 matrix product state method, the global states are written as a linear combination of entangled states, similar to TPSCI but mainly focusing on disjointed molecular units. A broad list of methods exists which focuses on forming the wave function of the full system in this clustered framework, including Block Correlated Coupled Cluster (BCCC) 36 and the related Tensor Product State Coupled Electron Pair-Type Approximations (TPS-CEPA), 37 the cMF-based coupled cluster, 38 the ab initio Frenkel−Davydov model, 39,40 the renormalized exciton model (REM), 41,42 the Block Interaction Product State (BIPS), 43 the comb-Tensor network states based approach by Li, 44 and the generalized and localized active space methods. 45−47 In this work, we extend our recently proposed TPSCI methodology 31 to provide near-FCI approximations to relatively large manifolds of excited states in a limited basis of active orbitals.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the Tensor Product Selected CI Method for Molecular Excited States

Braunscheidel,

Abraham,

Mayhall

2023

J. Phys. Chem. A

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In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited-state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons with respect to the extrapolated result (i.e., near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.

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Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions

Cited by 8 publications

References 87 publications

Properties of fermionic systems with the path-integral ground state method

Properties of fermionic systems with the path-integral ground state method

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

Generalization of the Tensor Product Selected CI Method for Molecular Excited States

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