Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants

Abstract

The few determinant (FED) methodology, introduced in our previous works for 1D lattices, is here adapted for the repulsive two-dimensional Hubbard model at half-filling and with finite doping fractions. Within this configuration mixing scheme, a given ground state with well defined spin and space group quantum numbers, is expanded in terms of a nonorthogonal symmetry-projected basis determined through chains of variation-after projection calculations. The results obtained for the ground state and correlation energies of half-filled and doped 4$\times$4, 6$\times$6, 8$\times$8, and 10$\times$10 lattices, as well as momentum distributions and spin-spin correlation functions in small lattices, compare well with those obtained using other state-of-the-art approximations. The structure of the intrinsic determinants resulting from the variational strategy is interpreted in terms of defects that encode information on the basic units of quantum fluctuations in the considered 2D systems. The varying nature of the underlying quantum fluctuations, reflected in a transition to a stripe regime for increasing onsite repulsions, is discussed using the intrinsic determinants belonging to a 16$\times$4 lattice with 56 electrons. Such a transition is further illustrated by computing spin-spin and charge-charge correlation functions with the corresponding multireference FED wave functions. In good agreement with previous studies, the analysis of the pairing correlation functions reveals a weak enhancement of the extended $s$-wave and d${}_{x^2-y^2}$ pairing modes. Given the quality of results here reported together with those previously obtained for 1D lattices and the parallelization properties of the FED scheme, we believe that symmetry projection techniques are very well suited for building ground state wave functions of correlated electronic systems, regardless of their dimensionality.

arXiv comment15 pages, 9 figures

References in corpus (53)

• The electronic properties of graphene
• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Correlated Electrons in High Temperature Superconductors
• Complexity in Strongly Correlated Electronic Systems
• Superconductivity in Iron Compounds
• Quantum Cluster Theories
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• A Mott insulator of fermionic atoms in an optical lattice
• Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Magnetism and its microscopic origin in iron-based high-temperature superconductors
• Self-energy-functional approach to systems of correlated electrons
• The Unexpected Properties of Alkali Metal Iron Selenide Superconductors
• Missing Quasiparticles and the Chemical Potential Puzzle in the Doping Evolution of the Cuprate Superconductors
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Fermionic Projected Entangled Pair States
• Projected Hartree-Fock Theory
• Correlations beyond the mean field in Magnesium isotopes: Angular momentum projection and configuration mixing
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Projected Quasiparticle Theory for Molecular Electronic Structure
• Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory
• Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Optimizing large parameter sets in variational quantum Monte Carlo
• Stripes on a 6-Leg Hubbard Ladder
• Absence of a Slater Transition in The Two-Dimensional Hubbard Model
• Optical conductivity of the half-filled Hubbard chain
• Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: the $J_1$--$J_2$--$J_3$ model
• Spin and charge order in doped Hubbard model: long-wavelength collective modes
• Electron correlation in solids via density embedding theory
• Symmetry in Auxiliary-Field Quantum Monte Carlo Calculations
• Stripe formation in doped Hubbard ladders
• Microscopic description of fission in Uranium isotopes with the Gogny energy density functional
• The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
• Microscopic description of quadrupole-octupole coupling in Sm and Gd isotopes with the Gogny Energy Density Functional
• Symmetry-projected Wave Functions in Quantum Monte Carlo Calculations
• Multi-component symmetry-projected approach for molecular ground state correlations
• Multi-reference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model
• Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part I: Energies, form factors, charge densities and mathematical sum rules
• Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems
• Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations
• Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part II: Spectral functions and spectroscopic factors
• Dynamical Cluster Approximation Employing FLEX as a Cluster Solver
• A symmetry-projected variational approach to the 1-dimensional Hubbard-model
• N-electron Slater determinants from non-unitary canonical transformations of fermion operators
• Exotic spin, charge and pairing correlations of the two-dimensional doped Hubbard model: a symmetry entangled mean-field approach
• Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model

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• Efficient computation of matrix elements of generic Slater determinants
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