精确保模随机时变Hartree-Fock

Limitations of Hartree-Fock with quantum resources

The Hartree-Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the fundamental Hartree-Fock problem is a natural target. While quantum computers and quantum simulation offer many prospects for the future of modern chemistry, the Hartree-Fock problem is not a likely candidate. We highlight this fact from a number of perspectives including computational complexity, practical examples, and the full characterization of the energy landscapes for simple systems…

Koopmans' theorem in statistical Hartree-Fock theory

In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field …

Implicit ladder summation in the Hartree-Fock-Bogoliubov approach

The fully variational Hartree Fock Bogoliubov approach for bosons is studied in the limit of zero range forces in two- and three-dimensions. The equation of state obtained in two-dimensions is expressed in a parametric form. It is shown that the $Λ$ potential permits to perform an implicit summation of the ladder diagrams without leaving the variational scheme, restoring thus the consistency of this approximation.

Simplified Hartree-Fock Computations on Second-Row Atoms

Simplified Hartree-Fock computations are carried out on the atoms He through Ne, using orthonormalized basis functions for the 1s, 2s and 2p orbitals dependent on three parameters. Using Mathematica with the new Apple M1 chip, computations require about 0.005 seconds of CPU time. Approximate energies within 1% of the best H-F values are thereby obtained, with an order of magnitude less computational effort.

Global Solutions of Hartree-Fock Theory and their Consequences for Strongly Correlated Quantum Systems

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 lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. For strongly correlated systems the SDP approach requires us to reassess the accuracy of the Hartree-Fock energies and densities from standard software packages for electronic structure theory. Calculations of the H$_{4}$ dimer and N$_{2}$ mol…

从Hartree和Hartree-Fock到Vlasov-Poisson方程的强半经典极限

Strong semiclassical limit from Hartree and Hartree-Fock to Vlasov-Poisson equation

本文研究了从Hartree和Hartree-Fock到Vlasov方程的半经典极限，在Schatten范数下证明了强拓扑中的显式界，并给出了费米子情形下交换项估计及收敛速率，适用于一般初始数据和任意固定时间区间。

Post-Hartree-Fock method in Quantum Chemistry for Quantum Computer

Quantum computational chemistry is a potential application of quantum computers that is expected to effectively solve several quantum-chemistry problems, particularly the electronic structure problem. Quantum computational chemistry can be compared to the conventional computational devices. This review comprehensively investigates the applications and overview of quantum computational chemistry, including a review of the Hartree-Fock method for quantum information scientists. Quantum algorithms, quantum phase estimation, and variational quantum eigensolver, have been applied to the post-Hartre…

量子Monte-Carlo方法与Hartree-Fock Bogoliubov态两体问题的精确处理

Quantum Monte-Carlo methods and exact treatment of the two-body problem with Hartree-Fock Bogoliubov states

在这篇文章中，我们证明了精确的两体问题可以用密度之间的量子跳跃来代替，记为$D=| Ψ_a \right> \left< Ψ_b |$，其中$| Ψ_a \right>$和$| Ψ_b \right>$对于不同的准粒子算符是真空。它表明，随机过程可以写为一个随机的时间依赖Hartree-Fock Bogoliubov理论（随机TDHFB）的广义密度${\cal R}$与$D$，其中${\cal R}^2 = {\cal R}$沿每个随机轨迹。

Matrix product states for Hartree-Fock-Bogoliubov wave functions

We provide an efficient and accurate method for converting Hartree-Fock-Bogoliubov wave functions into matrix product states (MPSs). These wave functions, also known as Bogoliubov vacua, exhibit a peculiar entanglement structure that the eigenvectors of the reduced density matrix are also Bogoliubov vacua. We exploit this important feature to obtain their optimal MPS approximation and derive an explicit formula for corresponding MPS matrices. The performance of our method is benchmarked with the Kitaev chain and the Majorana-Hubbard model on the honeycomb lattice. The approach facilitates the …