Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization

The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one-and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to hole doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak d-wave superconducting order in the ground state for the doping concentration less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25.

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“…We apply the wave function employed in the mVMC 25 as the reference wave function of tensor network states, which is expressed as,…”

Section: B Variational Wave Function Ansatzmentioning

confidence: 99%

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

et al. 2017

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“…JastrowGutzwiller correlation factors are also very popular as variational wave functions in quantum Monte Carlo and other applications [7][8][9][10][11][12][13][14][15]. Non-variational solutions have also been discussed in the literature.…”

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confidence: 99%

Lie algebraic similarity transformed Hamiltonians for lattice model systems

et al. 2015

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We present a class of Lie algebraic similarity transformations generated by exponentials of twobody on-site hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor n i↑ n i↓ , and twosite products of density (n i↑ + n i↓ ) and spin (n i↑ − n i↓ ) operators. The resulting non-hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the 1D and 2D repulsive Hubbard model where it yields accurate results for small and medium size interaction strengths.Introduction.-Hamiltonian similarity transformations are ubiquitous in many areas of physics, including electronic structure and condensed matter theories, and have been applied in a myriad of contexts [1][2][3][4][5][6]. JastrowGutzwiller correlation factors are also very popular as variational wave functions in quantum Monte Carlo and other applications [7][8][9][10][11][12][13][14][15]. Non-variational solutions have also been discussed in the literature. Tsuneyuki [16] presented a Hilbert space Jastrow method based on a Gutzwiller factor i n i↑ n i↓ and applied it to the 1D Hubbard model, minimizing its energy variance as in the transcorrelated method [17][18][19]. Neuscamman et al. [20] proposed many-body Jastrow correlators, diagonal in the lattice basis, and truncated them to a subset of sites matching a given pattern; these authors compared projective solutions with those obtained stochastically via Monte Carlo.Here, we consider Hamiltonian transformations of the form e −J He J based on hermitian correlators J built from general two-body products of on-site operators over the entire lattice. The transformations here are generated by density (charge), spin, and Gutzwiller factor correlators, including density-spin crossed terms. Similar Jastrowtype correlators have been extensively discussed in the literature but almost always in a variational context [10]. Our transformed Hamiltonian is non-hermitian but can be solved in mean-field via projective equations similar in spirit to those of coupled cluster theory [20,21]. In this sense, the model is an extension that fits under the generalized coupled cluster label [22][23][24]. The fundamental difference is that traditional coupled cluster is formulated with particle-hole excitations out of a reference determinant via a non-hermitian cluster operator; the present model is constructed with on-site hermitian correlators.The main result of this paper is the realization that the Hausdorff series resulting from the non-unitary similarity transformation e −J He J can be analytically summed. This result follows from Lie algebraic arguments [25] after recognizing that bot...

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“…Recent development in the VMC method allows us to deal with a large number of parameters. 80,123,126,127) Numerical techniques for optimizing many parameters are described in §4.2.5. By many parameters in the part of refined single-particle wavefunctions as well as in the part of correlation factors such as Gutzwiller factor to punish two electrons on the same Wannier orbital, it opens a way of simulating strongly correlated systems by substantially reducing the biases as we see below.…”

Section: Variational Monte Carlo Methodsmentioning

confidence: 99%

“…For lattice Fermion solvers, various methods as exact diagonalization, auxiliary field Monte Carlo (AFMC), 77) pathintegral renormalization group (PIRG), 78,79) density matrix renormalization group (DMRG), many-variable variational Monte Carlo (mVMC), 80) and Gaussian-basis Monte Carlo 81,82) have been developed, which are applicable when the models have the Hamiltonian expression eq. (71).…”

Section: Low-energy Solvermentioning

confidence: 99%

Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems

2010

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Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries and characterizations of strongly correlated electron materials and by requirements for understanding mechanisms of intriguing phenomena beyond a single-particle picture. A three-stage scheme is developed as renormalized multi-scale solvers (RMS) utilizing the hierarchical electronic structure in the energy space. It provides us with an ab initio downfolding of the global band structure into low-energy effective models followed by low-energy solvers for the models. The RMS method is illustrated with examples of several materials. In particular, we overview cases such as dynamics of semiconductors, transition metals and their compounds including iron-based superconductors and perovskite oxides, and organic conductors of -ET type.

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Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization

Cited by 151 publications

References 55 publications

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

Lie algebraic similarity transformed Hamiltonians for lattice model systems

Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems

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