Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states

Stokes, James; Moreno, Javier Robledo; Pnevmatikakis, Eftychios A.; Carleo, Giuseppe

doi:10.1103/physrevb.102.205122

Cited by 43 publications

(41 citation statements)

References 38 publications

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“…The choice of efficient optimization algorithms for parameter updates in variational Monte Carlo has historically been a complex issue and is still under active debate (see e.g. [1,9,11,18,[40][41][42][43]). Among these works, Ref.…”

Section: B Optimizermentioning

confidence: 99%

“…Deep learning techniques have recently impacted ab initio quantum chemistry by providing a new approach to the problem of tractable parameterization of high dimensional function spaces in quantum many-body problems. Over the past few years, a growing number of works [1][2][3][4][5][6][7][8][9][10][11] have demonstrated the use of neural networks in wavefunction approximation, with an increasing amount of importance placed on building symmetry constraints into models. In particular, several works [5,6,8,9,11] have recently applied neural networks to model antisymmetric wavefunctions.…”

Section: Introductionmentioning

confidence: 99%

“…Over the past few years, a growing number of works [1][2][3][4][5][6][7][8][9][10][11] have demonstrated the use of neural networks in wavefunction approximation, with an increasing amount of importance placed on building symmetry constraints into models. In particular, several works [5,6,8,9,11] have recently applied neural networks to model antisymmetric wavefunctions.…”

Section: Introductionmentioning

confidence: 99%

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Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

Lin¹,

Goldshlager²,

Lin³

2021

Preprint

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The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. This work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can significantly outperform the largest standard FermiNet calculation with 64 determinants, yielding an energy within 0.4 kcal/mol of the best available computational benchmark.

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Section: B Optimizermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

Lin¹,

Goldshlager²,

Lin³

2021

Preprint

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“…The remarkable success of variational states in the description of quantum spin systems unfortunately does not have a parallel in correlated systems of fermions, however. It is known, for example, that the natural mean-field analogue of direct-product states, the so-called Slater determinant (SD) states, fail to even qualitatively describe the thermodynamic limit of Fermi-Hubbard type Hamiltonians 3 and the development of systematically improvable neural-network-based trial wave functions is currently an active field of research both in second quantization [6][7][8] , and first quantization [9][10][11][12][13][14][15] . In the latter approach, the wave function amplitudes must be anti-symmetric functions of the particle configurations, while being able to capture correlations beyond the singleparticle Slater determinants.…”

Section: Introductionmentioning

confidence: 99%

“…In the latter approach, the wave function amplitudes must be anti-symmetric functions of the particle configurations, while being able to capture correlations beyond the singleparticle Slater determinants. This is typically achieved either by considering determinants of multi-particle orbitals 10,12,14 (backflow transformations), or by Slater determinants of single-particle orbitals multiplied by a neural-network Jastrow factor that depends on the lattice occupations 9,11 . Despite being universal in the lattice, the Slater neural-network Jastrow wave functions seem to struggle to get competitive energies in the strong coupling regime.…”

Section: Introductionmentioning

confidence: 99%

Fermionic Wave Functions from Neural-Network Constrained Hidden States

Moreno,

Carleo,

Georges

et al. 2021

Preprint

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We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving 'hidden' additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint which is optimized, together with the single-particle orbitals, using a neural network parametrization. This construction draws inspiration from the success of hidden particle representations 1 but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proven to be universal. We apply this construction to the ground state properties of the Hubbard model on the square lattice, achieving levels of accuracy which are competitive with and in some cases superior to state-of-the-art computational methods.

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