Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

Stella, Lorenzo; Attaccalite, Claudio; Sorella, Sandro; Rubio, Ángel

doi:10.1103/physrevb.84.245117

Cited by 92 publications

(119 citation statements)

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“…While previous theoretical studies on confined onedimensional fermions addressed the case of (typically small) harmonic traps [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65], in this Rapid Communication we considered a commensurate periodic potential, using sufficiently large system sizes to inspect the thermodynamic limit. On the one hand, this study provides new unbiased predictions for a paradigmatic model of strongly-correlated Fermi systems, which interpolates between Yang theory of the homogeneous Fermi gas and Lieb-Wu theory of the Hubbard model; on the other hand, it serves as a guide for possible new cold-atoms experiments aiming at observing antiferromagnetism beyond the tight-binding regime [30,66].…”

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confidence: 99%

One-dimensional repulsive Fermi gas in a tunable periodic potential

Pilati

Barbiero²,

Fazio

et al. 2017

Phys. Rev. A

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By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the TonksGirardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.Making unbiased predictions for the properties of strongly correlated Fermi systems is one of the major challenges in quantum physics research. One dimensional systems play a central role in this context since, on the one hand, correlations effects are more pronounced in low dimensions and, on the other hand, exact results have been derived in a few relevant cases [1]. Two such cases are the homogeneous Fermi gas, whose exact ground-state energy was first determined by Yang [2] via the Bethe Anstatz technique, and the single-band Hubbard model, whose solution was provided by Lieb and Wu [3]. These two paradigmatic models describe two opposite limits of realistic physical systems, which in general are neither perfectly homogeneous nor devoid of interband couplings. In the absence of exact analytical theories for the more realistic intermediate regime, developing unbiased computational techniques is of outmost importance. The experiments performed with ultracold atoms trapped in optical lattices (OLs) have emerged as the ideal playground to investigate quantum many-body phenomena in periodic potentials [4]. The intensity of the external periodic field can be easily varied by tuning a laser power, and also the interaction strength can by tuned exploiting Feshbach resonances [5]. This has recently allowed the remarkable observation of antiferromagnetic correlations in a controlled experimental setup, both in two and in one dimension [6][7][8][9][10][11][12]. The bulk of early research activity on OL systems focussed on deep OLs and weak interactions, where single-band tight-binding models are adequate [13]. Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the in...

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confidence: 99%

One-dimensional repulsive Fermi gas in a tunable periodic potential

Pilati

Barbiero²,

Fazio

et al. 2017

Phys. Rev. A

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“…The Hamiltonian as defined in Eq. (4) was used for the study of the symmetric stretching of the H 50 hydrogen chain, which is a commonly-used molecular model for strongly-correlated systems and which remains a challenging problem for conventional quantumchemistry methods [45][46][47][48].…”

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Efficient description of strongly correlated electrons with mean-field cost

et al. 2014

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We present an efficient approach to the electron correlation problem that is well-suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for the one-dimensional Hubbard model for different ring lengths, and for the non-relativistic quantum chemical Hamiltonian exploring the symmetric dissociation of the H50 hydrogen chain.The accurate description of the electron-electron interaction at the quantum-mechanical level is a key problem in condensed matter physics and quantum chemistry. Since most of the quantum many-body problems are extraordinarily difficult to solve exactly, different approximation schemes emerged [5][6][7][8][9], among which the density matrix renormalization group (DMRG) algorithm [10][11][12] gained a lot of popularity in both condensed matter physics [11] and quantum chemistry [13][14][15][16][17][18][19][20] over the last decade. Since the DMRG algorithm optimizes a matrix product state wavefunction, it is optimally suited for one-dimensional systems; though DMRG studies on higher-dimensional and compact systems have been reported [14,17,19,21]. Yet, novel theoretical approaches are desirable that can accurately describe strong correlation effects between electrons where the dimension of the Hilbert space exceeds the present-day limit of DMRG or general tensor-network approaches [22] allowing approximately 100 sites or 60 (spatial) orbitals, respectively.Another promising approach, suitable for larger strongly-correlated electronic systems, uses geminals (two-electron basis functions) as building blocks for the wavefunction [23][24][25][26][27][28][29][30]. One of the simplest practical geminal approaches is the antisymmetric product of 1-reference-orbital geminals (AP1roG) [31][32][33]. Unique among geminal methods, AP1roG can be rewritten as a fully general pair-coupled-cluster doubles wavefunc- * ayers@mcmaster.ca † dimitri.vanneck@ugent.be tion [34], i.e.where a † pσ and a pσ (σ = ↓, ↑) are the fermionic creation and annihilation operators, and |Φ 0 is some independent-particle wavefunction (usually the HartreeFock determinant). Indices i and a correspond to virtual and occupied sites (orbitals) with respect to |Φ 0 , P and K denote the number of electron pairs (P = N/2 with N being the total number of electrons) and orbitals, respectively, and {c a i } are the geminal coefficients. This wavefunction ansatz is size-extensive and has mean-field scaling, O P 2 (K − P ) 2 for the projected Schrödinger equation approach [31].To ensure size-consistency, however, it is necessary to optimize the one-electron basis functions [31], where all non-redundant orbital rotations span the occupiedoccupied, occupied-virtual, and virtual-virtual blocks with respect to the reference Slater determinant |Φ 0 . We have implemented a quadratically convergent algorithm: we minimize the energy with respect to the choice of the one-particle basis functions, subject to the constraint that the projected Schrödinger equati...

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“…However, many approximate numerical algorithms scale exponentially with system size if the quantum system contains strongly-correlated electrons. The most promising numerical approaches to treat strongly-correlated fermions are the Density Matrix Renormalization Group (DMRG) algorithm [5][6][7][8][9][10][11][12][13][14][15] and the quantum Monte Carlo (QMC) method [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Analysis of two-orbital correlations in wave functions restricted to electron-pair states

2016

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Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wavefunctions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the AP1roG method. Furthermore, we examine the effect of orbital rotations within the AP1roG model on correlations between orbital pairs.

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Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

Cited by 92 publications

References 44 publications

One-dimensional repulsive Fermi gas in a tunable periodic potential

One-dimensional repulsive Fermi gas in a tunable periodic potential

Efficient description of strongly correlated electrons with mean-field cost

Analysis of two-orbital correlations in wave functions restricted to electron-pair states

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